MinT - Best Known (59, 59+16, s)-Nets in Base 16

Best Known (59, 59+16, s)-Nets in Base 16

Digital (59, 75, 131071)-net over F₁₆, using

net defined by OOA [i] based on linear OOA(16⁷⁵, 131071, F₁₆, 16, 16) (dual of [(131071, 16), 2097061, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(16⁷⁵, 1048568, F₁₆, 16) (dual of [1048568, 1048493, 17]-code), using
  - discarding factors / shortening the dual code based on linear OA(16⁷⁵, 1048575, F₁₆, 16) (dual of [1048575, 1048500, 17]-code), using
    - 1 times truncation [i] based on linear OA(16⁷⁶, 1048576, F₁₆, 17) (dual of [1048576, 1048500, 18]-code), using
      - an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

Digital (59, 75, 933249)-net over F₁₆, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(16⁷⁵, 933249, F₁₆, 16) (dual of [933249, 933174, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(16⁷⁵, 1048575, F₁₆, 16) (dual of [1048575, 1048500, 17]-code), using
  - 1 times truncation [i] based on linear OA(16⁷⁶, 1048576, F₁₆, 17) (dual of [1048576, 1048500, 18]-code), using
    - an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 1048575Â = 16⁵âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]

There is no (59, 75, large)-net in base 16, because

14 times m-reduction [i] would yield (59, 61, large)-net in base 16, but
- mutually orthogonal hypercube bound [i]