MinT - Information on Result #548580

Information on Result #548580

There is no linear OA(3²⁴, 62, F₃, 15) (dual of [62, 38, 16]-code), because constructionÂ Y1 would yield

linear OA(3²³, 37, F₃, 15) (dual of [37, 14, 16]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3²², 28, F₃, 15) (dual of [28, 6, 16]-code), but
    - â€œHHMâ€ bound on codes from Brouwerâ€™s database [i]
  2. linear OA(3¹⁴, 37, F₃, 9) (dual of [37, 23, 10]-code), but
    - discarding factors / shortening the dual code would yield linear OA(3¹⁴, 31, F₃, 9) (dual of [31, 17, 10]-code), but
      - residual code [i] would yield linear OA(3⁵, 21, F₃, 3) (dual of [21, 16, 4]-code or 21-cap in PG(4,3)), but
        20 is the largest size of a cap in PG(4,Â 3) [i]
OA(3³⁸, 62, S₃, 25), but
- discarding factors would yield OA(3³⁸, 60, S₃, 25), but
  - the linear programming bound shows that MÂ â‰¥ 103845 619014 931091 288323 648431 / 71402 624384 > 3³⁸ [i]

Mode: Bound (linear).

None.

None.