MinT - Information on Result #599753

Information on Result #599753

There is no digital (30, 139, 164)-net over F₅, because extracting embedded orthogonal array would yield linear OA(5¹³⁹, 164, F₅, 109) (dual of [164, 25, 110]-code), but

constructionÂ Y1 [i] would yield
1. OA(5¹³⁸, 148, S₅, 109), but
  - the linear programming bound shows that MÂ â‰¥ 86 158555 819318 512642 331328 682663 835348 540649 443889 196923 328992 021307 026760 723601 910285 651683 807373 046875 / 29 425011 > 5¹³⁸ [i]
2. OA(5²⁵, 164, S₅, 16), but
  - discarding factors would yield OA(5²⁵, 148, S₅, 16), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 313081 833470 800945 > 5²⁵ [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 (30, 140, 164)-net over F₅	[i]		m-Reduction
2	No digital (30, 141, 164)-net over F₅	[i]
3	No digital (30, 142, 164)-net over F₅	[i]
4	No digital (30, 143, 164)-net over F₅	[i]
5	No digital (30, 144, 164)-net over F₅	[i]
6	No digital (30, 145, 164)-net over F₅	[i]
7	No digital (30, 146, 164)-net over F₅	[i]
8	No digital (30, 147, 164)-net over F₅	[i]
9	No digital (30, 148, 164)-net over F₅	[i]
10	No digital (30, 149, 164)-net over F₅	[i]