MinT - Best Known (48, 113, s)-Nets in Base 16

Best Known (48, 113, s)-Nets in Base 16

(48, 113, 243)-Net over F₁₆ — Constructive and digital

Digital (48, 113, 243)-net over F₁₆, using

net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
  - a function field by GarcÃa and Quoos [i]

(48, 113, 13952)-Net in Base 16 — Upper bound on s

There is no (48, 113, 13953)-net in base 16, because

1 times m-reduction [i] would yield (48, 112, 13953)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 727 206953 083789 710275 656968 824909 181669 951562 908495 490975 241297 697184 708556 476932 932608 195119 866384 981770 129239 523578 512038 525718 583916 > 16¹¹² [i]