MinT - Information on Result #599955

Information on Result #599955

There is no digital (1, 26, 123)-net over F₂₇, because extracting embedded orthogonal array would yield linear OA(27²⁶, 123, F₂₇, 25) (dual of [123, 97, 26]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(27²⁵, 29, F₂₇, 25) (dual of [29, 4, 26]-code or 29-arc in PG(24,27)), but
  - bound for MDS codes [i]
2. OA(27⁹⁷, 123, S₂₇, 94), but
  - discarding factors would yield OA(27⁹⁷, 103, S₂₇, 94), but
    - the linear programming bound shows that MÂ â‰¥ 128 911025 055144 003712 512083 846133 074073 104655 021247 977332 109220 807942 928575 240457 586722 133506 291651 511625 988777 715999 325631 713723 671307 153546 411869 / 17 583797 > 27⁹⁷ [i]

Mode: Bound (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

None.