MinT - Information on Result #1014478

Information on Result #1014478

Linear OOA(8¹¹⁷, 5592722, F₈, 3, 13) (dual of [(5592722, 3), 16778049, 14]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8¹⁹, 320, F₈, 3, 6) (dual of [(320, 3), 941, 7]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁵, 208, F₈, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(8⁵, 208, F₈, 2, 3) (dual of [(208, 2), 411, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁵, 208, F₈, 3) (dual of [208, 203, 4]-code or 208-cap in PG(4,8)), using
        caps completed using a computer search [i]
  2. linear OOA(8¹⁴, 160, F₈, 3, 6) (dual of [(160, 3), 466, 7]-NRT-code), using
    - extracting embedded OOA [i] based on digital (8, 14, 160)-net over F₈, using
      - trace code for nets [i] based on digital (1, 7, 80)-net over F₆₄, using
        net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
linear OOA(8⁹⁸, 5592402, F₈, 3, 13) (dual of [(5592402, 3), 16777108, 14]-NRT-code), using
- trace code [i] based on linear OOA(64⁴⁹, 2796201, F₆₄, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(64⁴⁹, large, F₆₄, 13) (dual of [large, large−49, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹¹⁷, 2796360, F₈, 15, 13) (dual of [(2796360, 15), 41945283, 14]-NRT-code)	[i]		OOA Folding and Stacking with Additional Row