MinT - Information on Result #3244665

Information on Result #3244665

Digital (33, 39, large)-net over F₆₄, using t-expansion based on digital (32, 39, large)-net over F₆₄, using

(u,Â u+v)-construction [i] based on
1. digital (4, 7, large)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64⁷, large, F₆₄, 3, 3), using
    - appending kth column [i] based on linear OOA(64⁷, large, F₆₄, 2, 3), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(64⁷, large, F₆₄, 3) (dual of [large, large−7, 4]-code), using
        product of projective cap with 64²-ovoid cap in AG(3,Â 64) [i] based on linear OA(64⁴, 4097, F₆₄, 3) (dual of [4097, 4093, 4]-code or 4097-cap in PG(3,64)), using
        ovoid in PG(3,Â 64) [i]
2. digital (25, 32, 5592401)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64³², 5592401, F₆₄, 9, 7) (dual of [(5592401, 9), 50331577, 8]-NRT-code), using
    - OOA stacking with additional row [i] based on linear OOA(64³², 5592402, F₆₄, 3, 7) (dual of [(5592402, 3), 16777174, 8]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(64⁷, large, F₆₄, 3, 3) (see above)
        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		Method
1	Digital (34, 40, large)-net over F₆₄	[i]	Net Duplication
2	Digital (35, 41, large)-net over F₆₄	[i]
3	Digital (36, 42, large)-net over F₆₄	[i]
4	Digital (37, 43, large)-net over F₆₄	[i]
5	Digital (38, 44, large)-net over F₆₄	[i]
6	Digital (39, 45, large)-net over F₆₄	[i]
7	Digital (40, 46, large)-net over F₆₄	[i]
8	Digital (41, 47, large)-net over F₆₄	[i]
9	Digital (42, 48, large)-net over F₆₄	[i]