MinT - Information on Result #547738

Information on Result #547738

There is no linear OA(3²⁷, 37, F₃, 18) (dual of [37, 10, 19]-code), because constructionÂ Y1 would yield

linear OA(3²⁶, 31, F₃, 18) (dual of [31, 5, 19]-code), but
- residual code [i] would yield linear OA(3⁸, 12, F₃, 6) (dual of [12, 4, 7]-code), but
  - residual code [i] would yield linear OA(3², 5, F₃, 2) (dual of [5, 3, 3]-code or 5-arc in PG(1,3)), but
    - improvement by Maruta on the Griesmer bound [i]
OA(3¹⁰, 37, S₃, 6), but
- discarding factors would yield OA(3¹⁰, 36, S₃, 6), but
  - the Rao or (dual) Hamming bound shows that MÂ â‰¥ 59713 > 3¹⁰ [i]

Mode: Bound (linear).

None.

None.