MinT - Best Known (114−67, 114, s)-Nets in Base 16

Best Known (114−67, 114, s)-Nets in Base 16

(114−67, 114, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 114, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 114, 225)-net over F₁₆, using
- net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
    - a function field by GarcÃa and Quoos [i]

(114−67, 114, 243)-Net over F₁₆ — Digital

Digital (47, 114, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 114, 243)-net over F₁₆, using
- net from sequence [i] based on digital (46, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 46 and N(F) ≥ 243, using
    - a curve from the manYPoints database [i]

(114−67, 114, 11635)-Net in Base 16 — Upper bound on s

There is no (47, 114, 11636)-net in base 16, because

1 times m-reduction [i] would yield (47, 113, 11636)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11647 655732 026568 089397 086035 033297 764080 649516 337427 643420 610401 738200 153758 714345 357796 158394 551277 317113 296198 621952 764123 637754 604621 > 16¹¹³ [i]