MinT - Best Known (110−64, 110, s)-Nets in Base 16

Best Known (110−64, 110, s)-Nets in Base 16

(110−64, 110, 225)-Net over F₁₆ — Constructive and digital

Digital (46, 110, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 110, 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]

(110−64, 110, 243)-Net over F₁₆ — Digital

Digital (46, 110, 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]

(110−64, 110, 11730)-Net in Base 16 — Upper bound on s

There is no (46, 110, 11731)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 846661 991894 382126 469451 076977 479020 011864 570212 952616 463910 492111 229591 558286 217257 157268 871340 089236 685084 788597 981792 186287 582606 > 16¹¹⁰ [i]