MinT - Information on Result #599926

Information on Result #599926

There is no digital (4, 104, 128)-net over F₂₅, because extracting embedded orthogonal array would yield linear OA(25¹⁰⁴, 128, F₂₅, 100) (dual of [128, 24, 101]-code), but

residual code [i] would yield linear OA(25⁴, 27, F₂₅, 4) (dual of [27, 23, 5]-code or 27-arc in PG(3,25)), but
- bound for MDS codes [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, 105, 128)-net over F₂₅	[i]	m-Reduction
2	No digital (4, 106, 128)-net over F₂₅	[i]
3	No digital (4, 107, 128)-net over F₂₅	[i]
4	No digital (4, 108, 128)-net over F₂₅	[i]
5	No digital (4, 109, 128)-net over F₂₅	[i]
6	No digital (4, 110, 128)-net over F₂₅	[i]
7	No digital (4, m, 128)-net over F₂₅ for arbitrarily large m	[i]	m-Reduction from Arbitrarily Large Net