MinT - Best Known (156, 156+24, s)-Nets in Base 4

Best Known (156, 156+24, s)-Nets in Base 4

Digital (156, 180, 87381)-net over F₄, using

net defined by OOA [i] based on linear OOA(4¹⁸⁰, 87381, F₄, 24, 24) (dual of [(87381, 24), 2096964, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(4¹⁸⁰, 1048572, F₄, 24) (dual of [1048572, 1048392, 25]-code), using
  - discarding factors / shortening the dual code based on linear OA(4¹⁸⁰, 1048576, F₄, 24) (dual of [1048576, 1048396, 25]-code), using
    - 1 times truncation [i] based on 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]

Digital (156, 180, 366882)-net over F₄, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(4¹⁸⁰, 366882, F₄, 2, 24) (dual of [(366882, 2), 733584, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁸⁰, 524288, F₄, 2, 24) (dual of [(524288, 2), 1048396, 25]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4¹⁸⁰, 1048576, F₄, 24) (dual of [1048576, 1048396, 25]-code), using
    - 1 times truncation [i] based on 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]

There is no (156, 180, large)-net in base 4, because

22 times m-reduction [i] would yield (156, 158, large)-net in base 4, but
- mutually orthogonal hypercube bound [i]