MinT - Information on Result #598811

Information on Result #598811

There is no digital (97, 183, 225)-net over F₂, because extracting embedded orthogonal array would yield linear OA(2¹⁸³, 225, F₂, 86) (dual of [225, 42, 87]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(2¹⁸², 211, F₂, 86) (dual of [211, 29, 87]-code), but
  - adding a parity check bit [i] would yield linear OA(2¹⁸³, 212, F₂, 87) (dual of [212, 29, 88]-code), but
    - â€œBKâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(2⁴², 225, S₂, 14), but
  - discarding factors would yield OA(2⁴², 219, S₂, 14), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 4 498367 189624 > 2⁴² [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 (97, 184, 225)-net over F₂	[i]		m-Reduction
2	No digital (97, 185, 225)-net over F₂	[i]
3	No digital (97, 186, 225)-net over F₂	[i]
4	No digital (97, 187, 225)-net over F₂	[i]
5	No digital (97, 188, 225)-net over F₂	[i]