MinT - Best Known (5, 5+39, s)-Nets in Base 16

Best Known (5, 5+39, s)-Nets in Base 16

(5, 5+39, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 44, 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+39, 258)-Net in Base 16 — Upper bound on s

There is no (5, 44, 259)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁴⁴, 259, S₁₆, 39), but
- the linear programming bound shows that MÂ â‰¥ 50 774228 000133 379999 225829 635218 451511 707870 599888 076338 819166 895840 828939 967031 893032 960000 / 526 270836 757774 539017 306203 501343 024669 > 16⁴⁴ [i]