MinT - Information on Result #1215231

Information on Result #1215231

Digital (95, 107, 2796460)-net over F₈, using (u,Â u+v)-construction based on

digital (11, 17, 260)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (2, 5, 208)-net over F₈, using
    - net defined by OOA [i] based on 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. 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]
digital (78, 90, 2796200)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁹⁰, 2796200, F₈, 14, 12) (dual of [(2796200, 14), 39146710, 13]-NRT-code), using
  - OOA 3-folding and stacking with additional row [i] based on linear OOA(8⁹⁰, 8388601, F₈, 2, 12) (dual of [(8388601, 2), 16777112, 13]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁹⁰, 8388602, F₈, 2, 12) (dual of [(8388602, 2), 16777114, 13]-NRT-code), using
      - trace code [i] based on linear OOA(64⁴⁵, 4194301, F₆₄, 2, 12) (dual of [(4194301, 2), 8388557, 13]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64⁴⁵, 8388602, F₆₄, 12) (dual of [8388602, 8388557, 13]-code), using
        discarding factors / shortening the dual code based on linear OA(64⁴⁵, large, F₆₄, 12) (dual of [large, large−45, 13]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (96, 108, 2796460)-net over F₈	[i]		Net Duplication