MinT - Information on Result #1842707

Information on Result #1842707

(54, 66, 349542)-net in base 16, using (u,Â u+v)-construction based on

digital (0, 6, 17)-net over F₁₆, using
- net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
    - the rational function field F₁₆(x) [i]
  - Niederreiter sequence [i]
(48, 60, 349525)-net in base 16, using
- net defined by OOA [i] based on OOA(16⁶⁰, 349525, S₁₆, 12, 12), using
  - OA 6-folding and stacking [i] based on OA(16⁶⁰, 2097150, S₁₆, 12), using
    - discarding factors based on OA(16⁶⁰, 2097155, S₁₆, 12), using
      - discarding parts of the base [i] based on linear OA(128³⁴, 2097155, F₁₂₈, 12) (dual of [2097155, 2097121, 13]-code), using
        constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
        linear OA(128³⁴, 2097152, F₁₂₈, 12) (dual of [2097152, 2097118, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(128³¹, 2097152, F₁₂₈, 11) (dual of [2097152, 2097121, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 128³âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(128⁰, 3, F₁₂₈, 0) (dual of [3, 3, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(128⁰, s, F₁₂₈, 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.

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.