MinT - Information on Result #1211320

Information on Result #1211320

Digital (193, 220, 80678)-net over F₄, using (u,Â u+v)-construction based on

digital (5, 18, 17)-net over F₄, using
- net from sequence [i] based on digital (5, 16)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]
digital (175, 202, 80661)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4²⁰², 80661, F₄, 27, 27) (dual of [(80661, 27), 2177645, 28]-NRT-code), using
  - OOA 13-folding and stacking with additional row [i] based on linear OA(4²⁰², 1048594, F₄, 27) (dual of [1048594, 1048392, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(4²⁰², 1048598, F₄, 27) (dual of [1048598, 1048396, 28]-code), using
      - constructionÂ X applied to C([0,13]) âŠ‚ C([0,12]) [i] based on
        linear OA(4²⁰¹, 1048577, F₄, 27) (dual of [1048577, 1048376, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
        linear OA(4¹⁸¹, 1048577, F₄, 25) (dual of [1048577, 1048396, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1048577Â | 4²⁰âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
        linear OA(4¹, 21, F₄, 1) (dual of [21, 20, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.