MinT - Best Known (120−75, 120, s)-Nets in Base 16

Best Known (120−75, 120, s)-Nets in Base 16

(120−75, 120, 225)-Net over F₁₆ — Constructive and digital

Digital (45, 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]

(120−75, 120, 242)-Net over F₁₆ — Digital

Digital (45, 120, 242)-net over F₁₆, using

net from sequence [i] based on digital (45, 241)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 45 and N(F) ≥ 242, using
  - a curve from the manYPoints database [i]

(120−75, 120, 7266)-Net in Base 16 — Upper bound on s

There is no (45, 120, 7267)-net in base 16, because

1 times m-reduction [i] would yield (45, 119, 7267)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 195858 159197 965646 003304 815539 145448 474738 992836 484763 117966 730409 278547 200334 076796 995775 212888 887677 260903 434848 547493 765975 503272 346988 192736 > 16¹¹⁹ [i]