MinT - Information on Result #547798

Information on Result #547798

There is no linear OA(3¹⁶², 172, F₃, 108) (dual of [172, 10, 109]-code), because constructionÂ Y1 would yield

linear OA(3¹⁶¹, 168, F₃, 108) (dual of [168, 7, 109]-code), but
- constructionÂ Y1 [i] would yield
  1. linear OA(3¹⁶⁰, 165, F₃, 108) (dual of [165, 5, 109]-code), but
    - Griesmer bound [i]
  2. linear OA(3⁷, 168, F₃, 3) (dual of [168, 161, 4]-code or 168-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, 172, S₃, 4), but
- the Rao or (dual) Hamming bound shows that MÂ â‰¥ 59169 > 3¹⁰ [i]

Mode: Bound (linear).

None.

The following results depend on this result:

	Result		This result only	Method
1	No linear OA(3¹⁶³, 180, F₃, 108) (dual of [180, 17, 109]-code)	[i]		ConstructionÂ Y1 (Bound)