MinT - Information on Result #1840883

Information on Result #1840883

(57, 70, 1398271)-net in base 32, using net defined by OOA based on OOA(32⁷⁰, 1398271, S₃₂, 14, 13), using

OOA 3-folding and stacking with additional row [i] based on OOA(32⁷⁰, 4194814, S₃₂, 2, 13), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(32¹¹, 513, F₃₂, 2, 6) (dual of [(513, 2), 1015, 7]-NRT-code), using
    - OOA 2-folding [i] based on linear OA(32¹¹, 1026, F₃₂, 6) (dual of [1026, 1015, 7]-code), using
      - constructionÂ X applied to C_e(5) âŠ‚ C_e(4) [i] based on
        linear OA(32¹¹, 1024, F₃₂, 6) (dual of [1024, 1013, 7]-code), using an extension C_e(5) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 6 [i]
        linear OA(32⁹, 1024, F₃₂, 5) (dual of [1024, 1015, 6]-code), using an extension C_e(4) of the primitive narrow-sense BCH-code C(I) with length 1023Â = 32²âˆ’1, defining interval IÂ =Â [1,4], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OA(32⁰, 2, F₃₂, 0) (dual of [2, 2, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(32⁰, s, F₃₂, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]
  2. OOA(32⁵⁹, 4194301, S₃₂, 2, 13), using
    - OOA 2-folding [i] based on OA(32⁵⁹, 8388602, S₃₂, 13), using
      - discarding factors based on OA(32⁵⁹, large, S₃₂, 13), using
        discarding parts of the base [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.

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.