MinT - Information on Result #558614

Information on Result #558614

There is no linear OOA(3²³⁹, 239, F₃, 2, 163) (dual of [(239, 2), 239, 164]-NRT-code), because 10 step m-reduction would yield linear OA(3²²⁹, 239, F₃, 153) (dual of [239, 10, 154]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3²²⁸, 235, F₃, 153) (dual of [235, 7, 154]-code), but
  - residual code [i] would yield linear OA(3⁷⁵, 81, F₃, 51) (dual of [81, 6, 52]-code), but
    - â€œMaâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(3¹⁰, 239, S₃, 4), but
  - discarding factors would yield OA(3¹⁰, 172, S₃, 4), but
    - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 59169 > 3¹⁰ [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(3²³⁹, 239, F₃, 3, 163) (dual of [(239, 3), 478, 164]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3²³⁹, 239, F₃, 4, 163) (dual of [(239, 4), 717, 164]-NRT-code)	[i]
3	No linear OOA(3²³⁹, 239, F₃, 5, 163) (dual of [(239, 5), 956, 164]-NRT-code)	[i]