MinT - Best Known (114−29, 114, s)-Nets in Base 16

Best Known (114−29, 114, s)-Nets in Base 16

Digital (85, 114, 9362)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16¹¹⁴, 9362, F₁₆, 29, 29) (dual of [(9362, 29), 271384, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(16¹¹⁴, 131069, F₁₆, 29) (dual of [131069, 130955, 30]-code), using
  - discarding factors / shortening the dual code based on linear OA(16¹¹⁴, 131074, F₁₆, 29) (dual of [131074, 130960, 30]-code), using
    - trace code [i] based on linear OA(256⁵⁷, 65537, F₂₅₆, 29) (dual of [65537, 65480, 30]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]

Digital (85, 114, 79745)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16¹¹⁴, 79745, F₁₆, 29) (dual of [79745, 79631, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(16¹¹⁴, 131074, F₁₆, 29) (dual of [131074, 130960, 30]-code), using
  - trace code [i] based on linear OA(256⁵⁷, 65537, F₂₅₆, 29) (dual of [65537, 65480, 30]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 65537Â | 256⁴âˆ’1, defining interval IÂ =Â [0,14], and minimum distance dÂ â‰¥ |{−14,−13,…,14}|+1Â =Â 30 (BCH-bound) [i]

There is no (85, 114, large)-net in base 16, because

27 times m-reduction [i] would yield (85, 87, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]