MinT - Best Known (52−47, 52, s)-Nets in Base 16

Best Known (52−47, 52, s)-Nets in Base 16

(52−47, 52, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 52, 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]

(52−47, 52, 239)-Net in Base 16 — Upper bound on s

There is no (5, 52, 240)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁵², 240, S₁₆, 47), but
- the linear programming bound shows that MÂ â‰¥ 2 604603 290367 203854 489641 973919 707250 233281 432812 190434 210962 336924 439348 115728 978046 384697 507840 / 6134 672235 456325 040138 601711 181213 > 16⁵² [i]