MinT - Information on Result #555636

Information on Result #555636

There is no linear OOA(3⁷⁷, 62, F₃, 2, 59) (dual of [(62, 2), 47, 60]-NRT-code), because 23 step m-reduction would yield linear OA(3⁵⁴, 62, F₃, 36) (dual of [62, 8, 37]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3⁵³, 58, F₃, 36) (dual of [58, 5, 37]-code), but
  - residual code [i] would yield linear OA(3¹⁷, 21, F₃, 12) (dual of [21, 4, 13]-code), but
    - â€œHNâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(3⁸, 62, S₃, 4), but
  - discarding factors would yield OA(3⁸, 58, S₃, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 6729 > 3⁸ [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		This result only	Method
1	No linear OOA(3⁷⁷, 62, F₃, 3, 59) (dual of [(62, 3), 109, 60]-NRT-code)	[i]		Depth Reduction
2	No linear OOA(3⁷⁷, 62, F₃, 4, 59) (dual of [(62, 4), 171, 60]-NRT-code)	[i]
3	No linear OOA(3⁷⁷, 62, F₃, 5, 59) (dual of [(62, 5), 233, 60]-NRT-code)	[i]