MinT - Best Known (90−23, 90, s)-Nets in Base 16

Best Known (90−23, 90, s)-Nets in Base 16

Digital (67, 90, 11915)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16⁹⁰, 11915, F₁₆, 23, 23) (dual of [(11915, 23), 273955, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(16⁹⁰, 131066, F₁₆, 23) (dual of [131066, 130976, 24]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁹⁰, 131074, F₁₆, 23) (dual of [131074, 130984, 24]-code), using
    - trace code [i] based on linear OA(256⁴⁵, 65537, F₂₅₆, 23) (dual of [65537, 65492, 24]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]

Digital (67, 90, 73369)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁹⁰, 73369, F₁₆, 23) (dual of [73369, 73279, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁹⁰, 131074, F₁₆, 23) (dual of [131074, 130984, 24]-code), using
  - trace code [i] based on linear OA(256⁴⁵, 65537, F₂₅₆, 23) (dual of [65537, 65492, 24]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]

There is no (67, 90, large)-net in base 16, because

21 times m-reduction [i] would yield (67, 69, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]