MinT - Best Known (37, 37+13, s)-Nets in Base 9

Best Known (37, 37+13, s)-Nets in Base 9

Digital (37, 50, 2187)-net over F₉, using

net defined by OOA [i] based on linear OOA(9⁵⁰, 2187, F₉, 13, 13) (dual of [(2187, 13), 28381, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(9⁵⁰, 13123, F₉, 13) (dual of [13123, 13073, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(9⁵⁰, 13124, F₉, 13) (dual of [13124, 13074, 14]-code), using
    - trace code [i] based on linear OA(81²⁵, 6562, F₈₁, 13) (dual of [6562, 6537, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Digital (37, 50, 10925)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁵⁰, 10925, F₉, 13) (dual of [10925, 10875, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(9⁵⁰, 13124, F₉, 13) (dual of [13124, 13074, 14]-code), using
  - trace code [i] based on linear OA(81²⁵, 6562, F₈₁, 13) (dual of [6562, 6537, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 6562Â | 81⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

There is no (37, 50, large)-net in base 9, because

11 times m-reduction [i] would yield (37, 39, large)-net in base 9, but
- mutually orthogonal hypercube bound [i]