MinT - Information on Result #599912

Information on Result #599912

There is no digital (6, 90, 150)-net over F₁₆, because extracting embedded orthogonal array would yield linear OA(16⁹⁰, 150, F₁₆, 84) (dual of [150, 60, 85]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(16⁸⁹, 94, F₁₆, 84) (dual of [94, 5, 85]-code), but
  - constructionÂ Y1 [i] would yield
    1. OA(16⁸⁸, 90, S₁₆, 84), but
      - 4 times truncation [i] would yield OA(16⁸⁴, 86, S₁₆, 80), but
        the (dual) Plotkin bound shows that MÂ â‰¥ 4 479489 484355 608421 114884 561136 888556 243290 994469 299069 799978 201927 583742 360321 890761 754986 543214 231552 / 27 > 16⁸⁴ [i]
    2. OA(16⁵, 94, S₁₆, 4), but
      - the linear programming bound shows that MÂ â‰¥ 2179 760128 / 2071 > 16⁵ [i]
2. OA(16⁶⁰, 150, S₁₆, 56), but
  - discarding factors would yield OA(16⁶⁰, 147, S₁₆, 56), but
    - the linear programming bound shows that MÂ â‰¥ 939765 966922 797477 814596 181274 291363 410391 878783 132568 319700 182987 088048 908156 194099 962624 995855 466829 447168 / 521248 355323 503233 415469 012835 684063 > 16⁶⁰ [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		This result only	Method
1	No digital (6, 91, 150)-net over F₁₆	[i]		m-Reduction