MinT - Best Known (50, 50+60, s)-Nets in Base 16

Best Known (50, 50+60, s)-Nets in Base 16

(50, 50+60, 243)-Net over F₁₆ — Constructive and digital

Digital (50, 110, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 110, 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]

(50, 50+60, 255)-Net over F₁₆ — Digital

Digital (50, 110, 255)-net over F₁₆, using

net from sequence [i] based on digital (50, 254)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 50 and N(F) ≥ 255, using
  - a curve from the manYPoints database [i]

(50, 50+60, 257)-Net in Base 16

(50, 110, 257)-net in base 16, using

base change [i] based on digital (28, 88, 257)-net over F₃₂, using
- net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
    - a curve from the manYPoints database [i]

(50, 50+60, 20867)-Net in Base 16 — Upper bound on s

There is no (50, 110, 20868)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 843139 179217 617352 635654 447897 667384 360251 011522 687983 664165 848866 244552 958069 878233 915482 202864 561332 596677 825770 964585 113021 770976 > 16¹¹⁰ [i]