MinT - Best Known (120−73, 120, s)-Nets in Base 16

Best Known (120−73, 120, s)-Nets in Base 16

(120−73, 120, 225)-Net over F₁₆ — Constructive and digital

Digital (47, 120, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 120, 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]

(120−73, 120, 243)-Net over F₁₆ — Digital

Digital (47, 120, 243)-net over F₁₆, using

t-expansion [i] based on digital (46, 120, 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]

(120−73, 120, 9077)-Net in Base 16 — Upper bound on s

There is no (47, 120, 9078)-net in base 16, because

1 times m-reduction [i] would yield (47, 119, 9078)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 195259 987319 362085 736598 198252 929049 993844 752895 388290 525202 223473 755943 104138 992271 837899 398957 049809 780065 967656 851074 175490 780764 834074 315121 > 16¹¹⁹ [i]