MinT - Information on Result #547801

Information on Result #547801

There is no linear OA(3¹⁶⁶, 176, F₃, 111) (dual of [176, 10, 112]-code), because constructionÂ Y1 would yield

linear OA(3¹⁶⁵, 172, F₃, 111) (dual of [172, 7, 112]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁶⁴, 169, F₃, 111) (dual of [169, 5, 112]-code), but
    - Griesmer bound [i]
  2. linear OA(3⁷, 172, F₃, 3) (dual of [172, 165, 4]-code or 172-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, 176, 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.