MinT - Information on Result #598834

Information on Result #598834

There is no digital (103, 195, 232)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2¹⁹⁵, 232, F₂, 92) (dual of [232, 37, 93]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(2¹⁹⁴, 220, F₂, 92) (dual of [220, 26, 93]-code), but
  - adding a parity check bit [i] would yield linear OA(2¹⁹⁵, 221, F₂, 93) (dual of [221, 26, 94]-code), but
    - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(2³⁷, 232, S₂, 12), but
  - discarding factors would yield OA(2³⁷, 217, S₂, 12), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 139173 045698 > 2³⁷ [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 (103, 196, 232)-net over F₂	[i]	m-Reduction
2	No digital (103, 197, 232)-net over F₂	[i]
3	No digital (103, 198, 232)-net over F₂	[i]