MinT - Information on Result #555328

Information on Result #555328

There is no linear OOA(3³⁷, 31, F₃, 2, 29) (dual of [(31, 2), 25, 30]-NRT-code), because 11 step m-reduction 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, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	No linear OOA(3³⁷, 31, F₃, 3, 29) (dual of [(31, 3), 56, 30]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3³⁷, 31, F₃, 4, 29) (dual of [(31, 4), 87, 30]-NRT-code)	[i]
3	No linear OOA(3³⁷, 31, F₃, 5, 29) (dual of [(31, 5), 118, 30]-NRT-code)	[i]