MinT - Best Known (58−53, 58, s)-Nets in Base 16

Best Known (58−53, 58, s)-Nets in Base 16

(58−53, 58, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 58, 49)-net over F₁₆, using

net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
  - a function field by SÃ©mirat [i]

(58−53, 58, 216)-Net in Base 16 — Upper bound on s

There is no (5, 58, 217)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁵⁸, 217, S₁₆, 53), but
- the linear programming bound shows that MÂ â‰¥ 1855 160421 485167 532697 230185 385114 241948 935576 221142 097060 485977 941929 761183 809173 556578 671056 111047 840712 622080 / 260456 341370 659788 255652 237699 894064 748133 > 16⁵⁸ [i]