MinT - Information on Result #1213534

Information on Result #1213534

Digital (45, 58, 531)-net over F₅, using (u,Â u+v)-construction based on

digital (1, 7, 10)-net over F₅, using
- net from sequence [i] based on digital (1, 9)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 1 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
digital (38, 51, 521)-net over F₅, using
- net defined by OOA [i] based on linear OOA(5⁵¹, 521, F₅, 13, 13) (dual of [(521, 13), 6722, 14]-NRT-code), using
  - OOA 6-folding and stacking with additional row [i] based on linear OA(5⁵¹, 3127, F₅, 13) (dual of [3127, 3076, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(5⁵¹, 3130, F₅, 13) (dual of [3130, 3079, 14]-code), using
      - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(5⁵¹, 3125, F₅, 13) (dual of [3125, 3074, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(5⁴⁶, 3125, F₅, 12) (dual of [3125, 3079, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 3124Â = 5⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(5⁰, 5, F₅, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(5⁰, s, F₅, 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

None.