MinT - Best Known (45−42, 45, s)-Nets in Base 16

Best Known (45−42, 45, s)-Nets in Base 16

(45−42, 45, 38)-Net over F₁₆ — Constructive and digital

Digital (3, 45, 38)-net over F₁₆, using

net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
  - a function field by SÃ©mirat [i]

(45−42, 45, 139)-Net in Base 16 — Upper bound on s

There is no (3, 45, 140)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁴⁵, 140, S₁₆, 42), but
- the linear programming bound shows that MÂ â‰¥ 177117 564936 019609 750790 688404 358861 415451 592472 428320 760049 440613 466112 / 112723 696702 567607 > 16⁴⁵ [i]