MinT - Information on Result #1215727

Information on Result #1215727

Digital (90, 112, 3007)-net over F₈, using (u,Â u+v)-construction based on

digital (5, 16, 28)-net over F₈, using
- net from sequence [i] based on digital (5, 27)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
    - a function field by SÃ©mirat [i]
digital (74, 96, 2979)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁹⁶, 2979, F₈, 22, 22) (dual of [(2979, 22), 65442, 23]-NRT-code), using
  - OA 11-folding and stacking [i] based on linear OA(8⁹⁶, 32769, F₈, 22) (dual of [32769, 32673, 23]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁹⁶, 32773, F₈, 22) (dual of [32773, 32677, 23]-code), using
      - constructionÂ X applied to C_e(21) âŠ‚ C_e(20) [i] based on
        linear OA(8⁹⁶, 32768, F₈, 22) (dual of [32768, 32672, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
        linear OA(8⁹¹, 32768, F₈, 21) (dual of [32768, 32677, 22]-code), using an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [i]
        linear OA(8⁰, 5, F₈, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (91, 113, 3007)-net over F₈	[i]		Net Duplication