MinT - Information on Result #1071993

Information on Result #1071993

Linear OOA(81⁵, 16318, F₈₁, 4, 3) (dual of [(16318, 4), 65267, 4]-NRT-code), using appending 1 arbitrary column based on linear OOA(81⁵, 16318, F₈₁, 3, 3) (dual of [(16318, 3), 48949, 4]-NRT-code), using

appending kth column [i] based on linear OOA(81⁵, 16318, F₈₁, 2, 3) (dual of [(16318, 2), 32631, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(81⁵, 16318, F₈₁, 3) (dual of [16318, 16313, 4]-code or 16318-cap in PG(4,81)), using
  - large caps in PG(4,Â b) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(81²⁶, 2812519, F₈₁, 4, 6) (dual of [(2812519, 4), 11250050, 7]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(81⁷⁹, 4207584, F₈₁, 4, 12) (dual of [(4207584, 4), 16830257, 13]-NRT-code)	[i]	Generalized (u,Â u+v)-Construction for OOAs
3	Linear OOA(81⁶³, 4210618, F₈₁, 4, 11) (dual of [(4210618, 4), 16842409, 12]-NRT-code)	[i]
4	Linear OOA(81⁵⁹, 4210618, F₈₁, 4, 10) (dual of [(4210618, 4), 16842413, 11]-NRT-code)	[i]