MinT - Best Known (51−46, 51, s)-Nets in Base 16

Best Known (51−46, 51, s)-Nets in Base 16

(51−46, 51, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 51, 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]

(51−46, 51, 241)-Net in Base 16 — Upper bound on s

There is no (5, 51, 242)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁵¹, 242, S₁₆, 46), but
- the linear programming bound shows that MÂ â‰¥ 2148 591701 535937 590268 263844 799420 841812 229277 625782 989002 957579 341541 699165 519827 172878 388310 310912 / 83 480374 838725 027966 829760 718317 045037 > 16⁵¹ [i]