MinT - Information on Result #1215313

Information on Result #1215313

Digital (159, 172, large)-net over F₈, using (u,Â u+v)-construction based on

digital (0, 6, 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 (153, 166, 8388602)-net over F₈, using
- trace code for nets [i] based on digital (70, 83, 4194301)-net over F₆₄, using
  - net defined by OOA [i] based on linear OOA(64⁸³, 4194301, F₆₄, 15, 13) (dual of [(4194301, 15), 62914432, 14]-NRT-code), using
    - OOA 2-folding and stacking with additional row [i] based on linear OOA(64⁸³, large, F₆₄, 3, 13), using
      - generalized (u,Â u+v)-construction [i] based on
        linear OOA(64¹³, 2796201, F₆₄, 3, 4) (dual of [(2796201, 3), 8388590, 5]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(64¹³, 4194301, F₆₄, 3, 4) (dual of [(4194301, 3), 12582890, 5]-NRT-code), using
        OA 2-folding and stacking [i] based on linear OA(64¹³, 8388602, F₆₄, 4) (dual of [8388602, 8388589, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(64¹³, large, F₆₄, 4) (dual of [large, large−13, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OOA(64²¹, 2796201, F₆₄, 3, 6) (dual of [(2796201, 3), 8388582, 7]-NRT-code), using
        OOA 3-folding [i] based on linear OA(64²¹, large, F₆₄, 6) (dual of [large, large−21, 7]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
        linear OOA(64⁴⁹, 2796201, F₆₄, 3, 13) (dual of [(2796201, 3), 8388554, 14]-NRT-code), using
        OOA 3-folding [i] based on linear OA(64⁴⁹, large, F₆₄, 13) (dual of [large, large−49, 14]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 64⁸âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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 (160, 172, large)-net over F₈	[i]	t-Expansion
2	Digital (160, 173, large)-net over F₈	[i]	Net Duplication
3	Digital (159, 171, large)-net over F₈	[i]	m-Reduction
4	Digital (159, 170, large)-net over F₈	[i]
5	Digital (159, 169, large)-net over F₈	[i]
6	Digital (159, 168, large)-net over F₈	[i]
7	Digital (159, 167, large)-net over F₈	[i]
8	Digital (159, 166, large)-net over F₈	[i]
9	Digital (159, 165, large)-net over F₈	[i]
10	Digital (159, 164, large)-net over F₈	[i]
11	Digital (159, 163, large)-net over F₈	[i]
12	Digital (159, 162, large)-net over F₈	[i]