MinT - Information on Result #599925

Information on Result #599925

There is no digital (4, 94, 164)-net over F₂₅, because extracting embedded orthogonal array would yield linear OA(25⁹⁴, 164, F₂₅, 90) (dual of [164, 70, 91]-code), but

constructionÂ Y1 [i] would yield
1. OA(25⁹³, 97, S₂₅, 90), but
  - the linear programming bound shows that MÂ â‰¥ 917 366046 106511 319204 310488 250559 166131 581647 062117 601772 786429 813888 045207 279411 397468 873458 869997 872255 908077 931962 907314 300537 109375 / 81263 > 25⁹³ [i]
2. linear OA(25⁷⁰, 164, F₂₅, 67) (dual of [164, 94, 68]-code), but
  - discarding factors / shortening the dual code would yield linear OA(25⁷⁰, 148, F₂₅, 67) (dual of [148, 78, 68]-code), but
    - constructionÂ Y1 [i] would yield
      1. OA(25⁶⁹, 73, S₂₅, 67), but
        the linear programming bound shows that MÂ â‰¥ 24178 564222 846123 668546 399721 917528 895562 151649 914153 732205 158997 548011 257094 913162 291049 957275 390625 / 7242 > 25⁶⁹ [i]
      2. linear OA(25⁷⁸, 148, F₂₅, 75) (dual of [148, 70, 76]-code), but
        discarding factors / shortening the dual code would yield linear OA(25⁷⁸, 103, F₂₅, 75) (dual of [103, 25, 76]-code), but
        residual code [i] would yield OA(25³, 27, S₂₅, 3), but
        bound for OAs with index unity [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

The following results depend on this result:

	Result		Method
1	No digital (4, 95, 164)-net over F₂₅	[i]	m-Reduction
2	No digital (4, 96, 164)-net over F₂₅	[i]
3	No digital (4, 97, 164)-net over F₂₅	[i]
4	No digital (4, 98, 164)-net over F₂₅	[i]
5	No digital (4, 99, 164)-net over F₂₅	[i]
6	No digital (4, 100, 164)-net over F₂₅	[i]
7	No digital (4, 101, 164)-net over F₂₅	[i]
8	No digital (4, 102, 164)-net over F₂₅	[i]
9	No digital (4, 103, 164)-net over F₂₅	[i]