MinT - Information on Result #598934

Information on Result #598934

There is no digital (8, 26, 31)-net over F₃, because extracting embedded orthogonal array would yield linear OA(3²⁶, 31, F₃, 18) (dual of [31, 5, 19]-code), but

residual code [i] would yield linear OA(3⁸, 12, F₃, 6) (dual of [12, 4, 7]-code), but
- residual code [i] would yield linear OA(3², 5, F₃, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,3)), but
  - improvement by Maruta on the Griesmer bound [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 (8, 27, 31)-net over F₃	[i]		m-Reduction
2	No digital (8, 28, 31)-net over F₃	[i]
3	No digital (8, 29, 31)-net over F₃	[i]
4	No digital (8, 30, 31)-net over F₃	[i]
5	No digital (8, 31, 31)-net over F₃	[i]
6	No digital (8, 32, 31)-net over F₃	[i]
7	No digital (8, 33, 31)-net over F₃	[i]
8	No digital (8, 34, 31)-net over F₃	[i]
9	No digital (8, 35, 31)-net over F₃	[i]
10	No digital (8, 36, 31)-net over F₃	[i]
11	No digital (8, 37, 31)-net over F₃	[i]
12	No digital (8, 38, 31)-net over F₃	[i]
13	No digital (8, 39, 31)-net over F₃	[i]