MinT - Information on Result #555301

Information on Result #555301

There is no linear OOA(3²⁹, 47, F₃, 2, 19) (dual of [(47, 2), 65, 20]-NRT-code), because 1 step m-reduction would yield linear OA(3²⁸, 47, F₃, 18) (dual of [47, 19, 19]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3²⁷, 35, F₃, 18) (dual of [35, 8, 19]-code), but
  - residual code [i] would yield linear OA(3⁹, 16, F₃, 6) (dual of [16, 7, 7]-code), but
    - â€œvE2â€ bound on codes from Brouwerâ€™s database [i]
2. linear OA(3¹⁹, 47, F₃, 12) (dual of [47, 28, 13]-code), but
  - discarding factors / shortening the dual code would yield linear OA(3¹⁹, 46, F₃, 12) (dual of [46, 27, 13]-code), but
    - residual code [i] would yield OA(3⁷, 33, S₃, 4), but
      - the linear programming bound shows that MÂ â‰¥ 64125 / 28 > 3⁷ [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(3²⁹, 47, F₃, 3, 19) (dual of [(47, 3), 112, 20]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3²⁹, 47, F₃, 4, 19) (dual of [(47, 4), 159, 20]-NRT-code)	[i]
3	No linear OOA(3²⁹, 47, F₃, 5, 19) (dual of [(47, 5), 206, 20]-NRT-code)	[i]