MinT - Information on Result #2698598

Information on Result #2698598

Linear OOA(8¹⁸, 260, F₈, 3, 6) (dual of [(260, 3), 762, 7]-NRT-code), using 8¹ times duplication based on linear OOA(8¹⁷, 260, F₈, 3, 6) (dual of [(260, 3), 763, 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(8¹², 130, F₈, 3, 6) (dual of [(130, 3), 378, 7]-NRT-code), using
  - extracting embedded OOA [i] based on digital (6, 12, 130)-net over F₈, using
    - trace code for nets [i] based on digital (0, 6, 65)-net over F₆₄, using
      - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [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

None.