This weapon is part of the set I use for my Nekros Prime Build. Here's my old Slash-Focused Build for anyone that prefers it for single target.

INTRODUCTION

Just throw some heat status here and there and watch everything melt thanks to Melee Influence and the various damage multipliers we have.

BUILD SPECIFICS

INCARNON CHOICES

1. Incarnon Form: This gives us the incarnon mode and is our only option at this tier. Besides the changes the incarnon form gives we also get +100% Melee Damage, +20% Sprint Speed, and +20% Bullet Jump.
2. Swordsman's Flourish: This increase Damage by +30. It is a base damage increase so it'll help with all our calculations. It also doubles combo chance so we can get to 12x combo faster.
3. Orokin [Reach]: This increases our range to 3.6m. To make up for not using the option with combo duration, we slot in Primary Dexterity and Secondary Dexterity to get 20 seconds of combo duration. Thanks to this we won't be forced to use [Primed Reach] or slot in Naramon as our focus school.
4. Subtle Force: +6% critical chance and +10% status chance. The thing is, this is an increase to your BASE critical/status chance, which gets affected by all multipliers later on, so it's a must.

GAS AND SLASH PROCS

For some odd reason, Gas procs seem to get exponentially stronger with Melee Afflictions whenever there's another DOT on an enemy. In this case my secondary gives electric procs while my companion gives heat procs. Anyway, my assumption is that it uses all the extra status created in the calculation before setting them to the limit of 10 stacks that Gas has. For this we have to understand all the multipliers included in melee calculations. These are:

• BASE DAMAGE: The [Hate] has a base 230 damage on normal attacks and 1380 damage on heavy attack. On top of that we get +30 damage because of our incarnon perk so that changes the values to 260 and 1410 respectively.

• DAMAGE MULTIPLIER: For our damage multiplier we'd have +265% from [Primed Pressure Point] and our incarnon mode, so we add on the multiplier to the base damage. You should always remember that these percentages are always added on top of the base, so 100% + 265% or (1 + 265%). Only mods that increase melee damage count for this calculation, so mods like Buzz Kill would do nothing.

• STATUS DAMAGE MULTIPLIER: Status damage mods work pretty similar to faction mods, multiplying their value in both steps of the calculation. There's a few exceptions where faction multiplier applies and status damage multiplier doesn't, but overal, a status damage mod is an exponential increase to our calcutations. Galvanized Elementalist gives us 80%, or (1 + 80%) when it comes to calculating.

• CRITICAL MULTIPLIER: The calculation here is a bit complex. by default we have 5.63x from the riven, but I have two Tauforged Violet Archon Shards on my warframe with 500+ energy for +150% critical damage, making it a 9.38x multiplier, then there's the +120% of the 4 stacks of Galvanized Steel making it 12.38x, and if we add the flat +1.2x of our companion's [Tenacious Bond] we'll get 13.58x, but we have to keep crit chance in mind. In warframe, when a weapon has over 100% crit chance it'll always crit, but it'll have a chance to do a higher tier crit, and that keeps going on for every 100% we add on to crit chance.
  Crit chance is multiplied by the base and added onto it. In this case the base is 30% but we add 6% for a 36% base thanks to our incarnon perk. Then we have +110% from Galvanized Steel, +241.6% from the riven, and +40% per combo multiplier starting from 2x from [Blood Rush]. This makes our calculations:
  36 x (1 + 110% + 241.6% + (40% x 11)) = 320.98% at 12x combo. This means all hits will do tier 3 red crits with a 21% chance of doing tier 4 crits.
  Now, 2 of those mods double their value when doing heavy attacks. That makes the calculations for heavy attacks:
  36 x (1 + ((110% + 241.6%) x 2) + (40% x 11)) = 447.55% at 12x combo. This means basically all heavy attacks will do tier 4 crits with a 48% chance of them doing tier 5 crits.
  The calculation for crit multiplier is 1 + Tier x (Crit Multiplier - 1).
  So on light attacks we get a 1 + (3 x (13.58 - 1)) = 38.74x damage multiplier, with a 21% chance of doing 1 + (4 x (13.58 - 1)) = 51.31x.
  And on heavy attacks we get a 1 + (4 x (13.58 - 1)) = 51.31x damage multiplier, with a 48% chance of doing 1 + (5 x (13.58 - 1)) = 63.89x.

• COMBO MULTIPLIER: For the combo multiplier we go up to 12x, which is easy enough considering we get double combo chance.

• FACTION MODS: We don't use faction mods in this build. If you wanted to use them, however, you could only replace [Weeping Wounds] with them. That'll make it so most of your light attacks won't proc slash, but your heavy attacks will deal over double your damage. I, however, recommend not using them, and instead subsuming Roar on your warframe if you REALLY want faction mods, since that works as a universal faction mod multiplier, even for enemies that have no specific factors you can mod for.

DAMAGE CALCULATION

Now that we explained how to calculate every variable for the equation let's move on to the damage calculation itself. Melee Afflictions works on 4 stages. Modded Base Damage, Status Average Damage, Afflictions Damage, and Afflictions Damage Tick.

MODDED BASE DAMAGE:

The modded base damage equation is: Base damage x Damage multiplier x Faction multiplier x Status Damage multiplier x Other multipliers.
That'd make our base modded damage for light attacks: 260 × (1 + 265%) x (1 + 80%) x 12 = 20,498.4 damage.

STATUS AVERAGE DAMAGE

This is the step where I assume Gas does its unique interaction. See, here the calculation for each status effect is (Sum of all Status Procs) / (Number of Status Procs). See, the issue is that Gas has a limit of 10 procs, and is the only DOT with that limit. The lift status also gives 12 procs instead of the usual 6, so we end up with 13 status procs. On top of that, our weapon has a 216% status chance at 12 combo, which means most of the time we'll proc 2 Gas status, which means 26 total.
That'd make our status average damage for the first hit of our neutral combo be: (20,498.4 x 26) / 10 = 53,295.84
And there you can see how every time we proc that status the value will increase exponentially. If we triggered lift status a second time with 2 status procs it'd be ((20,498.4 x 26) + (53,295.84 x 10)) / 10 = 106,591.68, though most enemies die on the first proc.
Keep in mind this is what I ASSUME happens, since I haven't found anywhere that explains this weird interaction in detail.

AFFLICTIONS DAMAGE:

Afflictions damage is basically the sum of all Status Average Damage multiplied by Faction multiplier. Let's assume there's an electricity proc doing 2500 damage per tick.
That'd make the calculations be 53,295.84 + 2,500 = 55,795.84

AFFLICTIONS DAMAGE TICK:

Lastly is the damage thick, which is Afflictions Damage x Status Effect multiplier x Faction multiplier x Status Damage multiplier. Faction and Status damage multipliers don't apply to heat unless they come from the weapon, sadly. This will end up with:
10 stacks of gas, doing 55,795.84 x 0.5 x (1 + 0.8) = 50,216.256
24 stacks of electric, doing 55,795.84 x 0.5 x (1 + 0.8) = 50,216.256
Considering gas and electric deal ticks immediately, as soon as you proc 2 gas with your first hit it'd deal (50,216.256 x 10) + (50,216.256 x 24) = 1,707,352.704 tick damage. The more different status DOTs there are, the bigger the damage will be.
For example, in the same calculation, let's assume the enemy has a slash, heat, electricity, and toxin proc and we proc 2 gas. That'd make the calculation end up as (35,151.3792 x 24) + (27,897.92 x 24) + (50,216.256 x 24) + (50,216.256 x 24) + (50,216.256 x 10) = 4,425,726.0288 tick damage per second. This might not be exactly accurate, since interactions with Melee Afflictions aren't that well calculated, but this is just a way to show how excessive the damage can get.

RIVEN:

The riven is quite important to this build, sadly. If you really wanted to replace it it should be with either a faction mod, attack speed mod, or more crit damage.