MinT - Information on Result #558231

Information on Result #558231

There is no linear OOA(3²²⁸, 203, F₃, 2, 164) (dual of [(203, 2), 178, 165]-NRT-code), because 35 step m-reduction would yield linear OA(3¹⁹³, 203, F₃, 129) (dual of [203, 10, 130]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁹², 199, F₃, 129) (dual of [199, 7, 130]-code), but
  - residual code [i] would yield linear OA(3⁶³, 69, F₃, 43) (dual of [69, 6, 44]-code), but
    - â€œMaâ€ bound on codes from Brouwerâ€™s database [i]
2. OA(3¹⁰, 203, 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(3²²⁸, 203, F₃, 3, 164) (dual of [(203, 3), 381, 165]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3²²⁸, 203, F₃, 4, 164) (dual of [(203, 4), 584, 165]-NRT-code)	[i]
3	No linear OOA(3²²⁸, 203, F₃, 5, 164) (dual of [(203, 5), 787, 165]-NRT-code)	[i]