MinT - Information on Result #1215208

Information on Result #1215208

Digital (124, 135, large)-net over F₈, using (u,Â u+v)-construction based on

digital (0, 5, 9)-net over F₈, using
- net from sequence [i] based on digital (0, 8)-sequence over F₈, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 0 and N(F) ≥ 9, using
    - the rational function field F₈(x) [i]
  - Niederreiter sequence [i]
digital (119, 130, 8388602)-net over F₈, using
- trace code for nets [i] based on digital (54, 65, 4194301)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64⁶⁵, 4194301, F₆₄, 15, 11) (dual of [(4194301, 15), 62914450, 12]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁶⁵, large, F₆₄, 3, 11), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(64⁷, 2796201, F₆₄, 3, 3) (dual of [(2796201, 3), 8388596, 4]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64⁷, 8388602, F₆₄, 3, 3) (dual of [(8388602, 3), 25165799, 4]-NRT-code), using
        OOA stacking with additional row [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]
        linear OOA(64¹⁷, 2796201, F₆₄, 3, 5) (dual of [(2796201, 3), 8388586, 6]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64¹⁷, 4194301, F₆₄, 3, 5) (dual of [(4194301, 3), 12582886, 6]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OA(64¹⁷, large, F₆₄, 5) (dual of [large, large−17, 6]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,2], and minimum distance dÂ â‰¥ |{−2,−1,0,1,2}|+1Â =Â 6 (BCH-bound) [i]
        linear OOA(64⁴¹, 2796201, F₆₄, 3, 11) (dual of [(2796201, 3), 8388562, 12]-NRT-code), using
        OOA 3-folding [i] based on linear OA(64⁴¹, large, F₆₄, 11) (dual of [large, large−41, 12]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,5], and minimum distance dÂ â‰¥ |{−5,−4,…,5}|+1Â =Â 12 (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 (125, 135, large)-net over F₈	[i]	t-Expansion
2	Digital (125, 136, large)-net over F₈	[i]	Net Duplication
3	Digital (126, 137, large)-net over F₈	[i]
4	Digital (127, 138, large)-net over F₈	[i]
5	Digital (128, 139, large)-net over F₈	[i]
6	Digital (129, 140, large)-net over F₈	[i]
7	Digital (130, 141, large)-net over F₈	[i]
8	Digital (131, 142, large)-net over F₈	[i]
9	Digital (132, 143, large)-net over F₈	[i]
10	Digital (124, 134, large)-net over F₈	[i]	m-Reduction
11	Digital (124, 133, large)-net over F₈	[i]
12	Digital (124, 132, large)-net over F₈	[i]
13	Digital (124, 131, large)-net over F₈	[i]
14	Digital (124, 130, large)-net over F₈	[i]
15	Digital (124, 129, large)-net over F₈	[i]
16	Digital (124, 128, large)-net over F₈	[i]
17	Digital (124, 127, large)-net over F₈	[i]