MinT - Information on Result #1757837

Information on Result #1757837

Digital (216, 233, 2098676)-net over F₂, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(2²³³, 2098676, F₂, 4, 17) (dual of [(2098676, 4), 8394471, 18]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(2⁴⁸, 1526, F₂, 4, 8) (dual of [(1526, 4), 6056, 9]-NRT-code), using
  - embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(2⁴⁸, 1526, F₂, 2, 8) (dual of [(1526, 2), 3004, 9]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(2⁴⁸, 2048, F₂, 2, 8) (dual of [(2048, 2), 4048, 9]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(2⁴⁸, 4096, F₂, 8) (dual of [4096, 4048, 9]-code), using
        1 times truncation [i] based on linear OA(2⁴⁹, 4097, F₂, 9) (dual of [4097, 4048, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 4097Â | 2²⁴âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [i]
2. linear OOA(2¹⁸⁵, 2097150, F₂, 4, 17) (dual of [(2097150, 4), 8388415, 18]-NRT-code), using
  - OOA 4-folding [i] based on linear OA(2¹⁸⁵, 8388600, F₂, 17) (dual of [8388600, 8388415, 18]-code), using
    - discarding factors / shortening the dual code based on linear OA(2¹⁸⁵, large, F₂, 17) (dual of [large, large−185, 18]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 8388609Â | 2⁴⁶âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]

Mode: 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.