MinT - Best Known (5, 5+63, s)-Nets in Base 16

Best Known (5, 5+63, s)-Nets in Base 16

(5, 5+63, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 68, 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]

(5, 5+63, 185)-Net in Base 16 — Upper bound on s

There is no (5, 68, 186)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁶⁸, 186, S₁₆, 63), but
- the linear programming bound shows that MÂ â‰¥ 52442 430410 589069 939312 443952 424353 167591 346016 655200 750231 600527 733014 040987 516413 277672 085994 184874 599044 400177 935969 943552 / 6 807974 242648 082061 193806 588990 089459 087455 > 16⁶⁸ [i]