MinT - Best Known (37, 50, s)-Nets in Base 16

Best Known (37, 50, s)-Nets in Base 16

Digital (37, 50, 21845)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16⁵⁰, 21845, F₁₆, 13, 13) (dual of [(21845, 13), 283935, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(16⁵⁰, 131071, F₁₆, 13) (dual of [131071, 131021, 14]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁵⁰, 131074, F₁₆, 13) (dual of [131074, 131024, 14]-code), using
    - trace code [i] based on linear OA(256²⁵, 65537, F₂₅₆, 13) (dual of [65537, 65512, 14]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (BCH-bound) [i]

Digital (37, 50, 75631)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁵⁰, 75631, F₁₆, 13) (dual of [75631, 75581, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁵⁰, 131074, F₁₆, 13) (dual of [131074, 131024, 14]-code), using
  - trace code [i] based on linear OA(256²⁵, 65537, F₂₅₆, 13) (dual of [65537, 65512, 14]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’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 16, because

11 times m-reduction [i] would yield (37, 39, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]