MinT - Information on Result #3171829

Information on Result #3171829

Digital (55, 59, large)-net over F₈, using 3 times m-reduction based on digital (55, 62, large)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 12, 2931457)-net over F₈, using
  - net defined by OOA [i] based on linear OOA(8¹², 2931457, F₈, 3, 3) (dual of [(2931457, 3), 8794359, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(8¹², 2931457, F₈, 2, 3) (dual of [(2931457, 2), 5862902, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8¹², 2931457, F₈, 3) (dual of [2931457, 2931445, 4]-code or 2931457-cap in PG(11,8)), using
        product of projective cap with cap in AG(5,Â 8) [i] based on linear OA(8⁷, 4224, F₈, 3) (dual of [4224, 4217, 4]-code or 4224-cap in PG(6,8)), using
        product of two caps with tangent hyperplane [i]
2. digital (43, 50, 5592401)-net over F₈, using
  - net defined by OOA [i] based on linear OOA(8⁵⁰, 5592401, F₈, 9, 7) (dual of [(5592401, 9), 50331559, 8]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(8⁵⁰, 5592402, F₈, 3, 7) (dual of [(5592402, 3), 16777156, 8]-NRT-code), using
      - trace code [i] based on linear OOA(64²⁵, 2796201, F₆₄, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
        OOA 3-folding [i] based on linear OA(64²⁵, large, F₆₄, 7) (dual of [large, large−25, 8]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,3], and minimum distance dÂ â‰¥ |{−3,−2,…,3}|+1Â =Â 8 (BCH-bound) [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (56, 59, large)-net over F₈	[i]		t-Expansion