MinT - Information on Result #1858741

Information on Result #1858741

There is no digital (4, m, 128)-net over F₂₅ for arbitrarily large m, because m-reduction would yield digital (4, 104, 128)-net over F₂₅, but

extracting embedded orthogonal array [i] 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).

Show details for fixed m and s, m and t, t and s.

None.

The following results depend on this result:

	Result		Method
1	No digital (4, 127)-sequence over F₂₅	[i]	Net from Sequence
2	No digital (4, 4+k, 128)-net over F₂₅ for arbitrarily large k	[i]	Logical Equivalence (for Nets with Unbounded m)
3	No digital (4, m, 128)-net over F₂₅ with unbounded m	[i]	Logical Equivalence (for Nets with Unbounded m)