MinT - Best Known (5, 5+36, s)-Nets in Base 16

Best Known (5, 5+36, s)-Nets in Base 16

(5, 5+36, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 41, 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+36, 260)-Net in Base 16 — Upper bound on s

There is no (5, 41, 261)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁴¹, 261, S₁₆, 36), but
- the linear programming bound shows that MÂ â‰¥ 26553 459104 854432 103318 340707 601087 035638 954440 703001 598239 410109 388771 012576 981024 768000 / 1121 449709 482315 003912 206862 750142 670001 > 16⁴¹ [i]