MinT - Information on Result #547803

Information on Result #547803

There is no linear OA(3¹⁷⁰, 180, F₃, 114) (dual of [180, 10, 115]-code), because constructionÂ Y1 would yield

linear OA(3¹⁶⁹, 176, F₃, 114) (dual of [176, 7, 115]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁶⁸, 173, F₃, 114) (dual of [173, 5, 115]-code), but
    - Griesmer bound [i]
  2. linear OA(3⁷, 176, F₃, 3) (dual of [176, 169, 4]-code or 176-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, 180, 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.