MinT - Information on Result #556923

Information on Result #556923

There is no linear OOA(3¹⁷³, 117, F₃, 2, 137) (dual of [(117, 2), 61, 138]-NRT-code), because 65 step m-reduction would yield linear OA(3¹⁰⁸, 117, F₃, 72) (dual of [117, 9, 73]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁰⁷, 113, F₃, 72) (dual of [113, 6, 73]-code), but
  - residual code [i] would yield linear OA(3³⁵, 40, F₃, 24) (dual of [40, 5, 25]-code), but
    - â€œvE1â€ bound on codes from Brouwerâ€™s database [i]
2. OA(3⁹, 117, S₃, 4), but
  - discarding factors would yield OA(3⁹, 100, S₃, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 20001 > 3⁹ [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(3¹⁷³, 117, F₃, 3, 137) (dual of [(117, 3), 178, 138]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3¹⁷³, 117, F₃, 4, 137) (dual of [(117, 4), 295, 138]-NRT-code)	[i]
3	No linear OOA(3¹⁷³, 117, F₃, 5, 137) (dual of [(117, 5), 412, 138]-NRT-code)	[i]