MinT - Information on Result #3226560

Information on Result #3226560

Digital (61, 64, large)-net over F₈, using t-expansion based on digital (57, 64, large)-net over F₈, using

trace code for nets [i] based on 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
      1. 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. 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 (62, 65, large)-net over F₈	[i]		Net Duplication
2	Digital (63, 66, large)-net over F₈	[i]
3	Digital (64, 67, large)-net over F₈	[i]
4	Digital (65, 68, large)-net over F₈	[i]
5	Digital (66, 69, large)-net over F₈	[i]
6	Digital (67, 70, large)-net over F₈	[i]
7	Digital (68, 71, large)-net over F₈	[i]
8	Digital (69, 72, large)-net over F₈	[i]
9	Digital (70, 73, large)-net over F₈	[i]
10	Digital (71, 74, large)-net over F₈	[i]
11	Digital (72, 75, large)-net over F₈	[i]
12	Digital (73, 76, large)-net over F₈	[i]
13	Digital (74, 77, large)-net over F₈	[i]
14	Digital (75, 78, large)-net over F₈	[i]
15	Digital (76, 79, large)-net over F₈	[i]