MinT - Information on Result #548631

Information on Result #548631

There is no linear OA(5²⁶, 64, F₅, 20) (dual of [64, 38, 21]-code), because constructionÂ Y1 would yield

linear OA(5²⁵, 34, F₅, 20) (dual of [34, 9, 21]-code), but
- residual code [i] would yield linear OA(5⁵, 13, F₅, 4) (dual of [13, 8, 5]-code), but
  - â€œBouâ€ bound on codes from Brouwerâ€™s database [i]
linear OA(5³⁸, 64, F₅, 30) (dual of [64, 26, 31]-code), but
- discarding factors / shortening the dual code would yield linear OA(5³⁸, 61, F₅, 30) (dual of [61, 23, 31]-code), but
  - constructionÂ Y1 [i] would yield
    1. linear OA(5³⁷, 43, F₅, 30) (dual of [43, 6, 31]-code), but
      - residual code [i] would yield linear OA(5⁷, 12, F₅, 6) (dual of [12, 5, 7]-code), but
        a result by Dodunekov and Landjev [i]
    2. OA(5²³, 61, S₅, 18), but
      - the linear programming bound shows that MÂ â‰¥ 6321 833259 448409 889221 191406 250000 / 502952 782605 714137 > 5²³ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		Method
1	No linear OA(5²⁷, 65, F₅, 21) (dual of [65, 38, 22]-code)	[i]	Truncation
2	No linear OOA(5²⁷, 64, F₅, 2, 21) (dual of [(64, 2), 101, 22]-NRT-code)	[i]	m-Reduction for OOAs
3	No linear OOA(5²⁸, 64, F₅, 2, 22) (dual of [(64, 2), 100, 23]-NRT-code)	[i]	m-Reduction for OOAs
4	No linear OOA(5²⁶, 64, F₅, 2, 20) (dual of [(64, 2), 102, 21]-NRT-code)	[i]	Depth Reduction
5	No linear OOA(5²⁶, 64, F₅, 3, 20) (dual of [(64, 3), 166, 21]-NRT-code)	[i]	Depth Reduction
6	No digital (6, 26, 64)-net over F₅	[i]	Extracting Embedded Orthogonal Array