MinT - Information on Result #1835315

Information on Result #1835315

OOA(8²⁴, 771, S₈, 3, 7), using extracting embedded OOA based on (17, 24, 771)-net in base 8, using

base change [i] based on digital (11, 18, 771)-net over F₁₆, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 4, 257)-net over F₁₆, using
    - net defined by OOA [i] based on linear OOA(16⁴, 257, F₁₆, 3, 3) (dual of [(257, 3), 767, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(16⁴, 257, F₁₆, 2, 3) (dual of [(257, 2), 510, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(16⁴, 257, F₁₆, 3) (dual of [257, 253, 4]-code or 257-cap in PG(3,16)), using
        ovoid in PG(3,Â 16) [i]
  2. digital (7, 14, 514)-net over F₁₆, using
    - trace code for nets [i] based on digital (0, 7, 257)-net over F₂₅₆, using
      - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
        Niederreiter sequence [i]

Mode: Constructive.

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		This result only	Method
1	OOA(8¹³⁰, 5593173, S₈, 3, 14)	[i]		(u,Â u+v)-Construction for OOAs
2	OOA(8¹³⁸, 5593173, S₈, 3, 15)	[i]		(u,Â u+v)-Construction for OOAs