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

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

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

Digital (5, 63, 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, 63, 209)-Net in Base 16 — Upper bound on s

There is no (5, 63, 210)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁶³, 210, S₁₆, 58), but
- the linear programming bound shows that MÂ â‰¥ 122 600872 493649 393319 484703 818591 621506 641480 876126 404933 857080 325519 975626 387608 819677 513375 810207 924477 675599 560704 / 16238 551342 924342 041531 482298 887222 269393 > 16⁶³ [i]