MinT - Information on Result #547805

Information on Result #547805

There is no linear OA(3¹⁷⁵, 185, F₃, 117) (dual of [185, 10, 118]-code), because constructionÂ Y1 would yield

linear OA(3¹⁷⁴, 181, F₃, 117) (dual of [181, 7, 118]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁷³, 178, F₃, 117) (dual of [178, 5, 118]-code), but
    - Griesmer bound [i]
  2. linear OA(3⁷, 181, F₃, 3) (dual of [181, 174, 4]-code or 181-cap in PG(6,3)), but
    - discarding factors / shortening the dual code would yield linear OA(3⁷, 137, F₃, 3) (dual of [137, 130, 4]-code or 137-cap in PG(6,3)), but
      - a result by BarÃ¡t, Edel, Hill, and Storme [i]
OA(3¹⁰, 185, 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).

None.

None.