MinT - Information on Result #556749

Information on Result #556749

There is no linear OOA(3¹⁶³, 171, F₃, 2, 109) (dual of [(171, 2), 179, 110]-NRT-code), because 1 step m-reduction would yield linear OA(3¹⁶², 171, F₃, 108) (dual of [171, 9, 109]-code), but

constructionÂ Y1 [i] would yield
1. linear OA(3¹⁶¹, 167, F₃, 108) (dual of [167, 6, 109]-code), but
  - residual code [i] would yield 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(3⁹, 171, 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(3¹⁶³, 171, F₃, 3, 109) (dual of [(171, 3), 350, 110]-NRT-code)	[i]	Depth Reduction
2	No linear OOA(3¹⁶³, 171, F₃, 4, 109) (dual of [(171, 4), 521, 110]-NRT-code)	[i]
3	No linear OOA(3¹⁶³, 171, F₃, 5, 109) (dual of [(171, 5), 692, 110]-NRT-code)	[i]