MinT - Information on Result #1205431

Information on Result #1205431

Digital (57, 64, large)-net over F₈, using trace code for nets 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 (58, 64, large)-net over F₈	[i]		t-Expansion
2	Digital (59, 64, large)-net over F₈	[i]
3	Digital (60, 64, large)-net over F₈	[i]
4	Digital (61, 64, large)-net over F₈	[i]
5	Digital (58, 65, large)-net over F₈	[i]		Net Duplication
6	Digital (59, 66, large)-net over F₈	[i]
7	Digital (60, 67, large)-net over F₈	[i]
8	Digital (61, 68, large)-net over F₈	[i]
9	Digital (62, 69, large)-net over F₈	[i]
10	Digital (63, 70, large)-net over F₈	[i]
11	Digital (64, 71, large)-net over F₈	[i]
12	Digital (65, 72, large)-net over F₈	[i]
13	Digital (66, 73, large)-net over F₈	[i]
14	Digital (67, 74, large)-net over F₈	[i]
15	Digital (68, 75, large)-net over F₈	[i]
16	Digital (69, 76, large)-net over F₈	[i]
17	Digital (70, 77, large)-net over F₈	[i]
18	Digital (71, 78, large)-net over F₈	[i]
19	Digital (72, 79, large)-net over F₈	[i]
20	Digital (73, 80, large)-net over F₈	[i]
21	Digital (74, 81, large)-net over F₈	[i]
22	Digital (75, 82, large)-net over F₈	[i]
23	Digital (76, 83, large)-net over F₈	[i]
24	Digital (57, 63, large)-net over F₈	[i]		m-Reduction
25	Digital (57, 62, large)-net over F₈	[i]
26	Digital (57, 61, large)-net over F₈	[i]
27	Digital (57, 60, large)-net over F₈	[i]