MinT - Best Known (15, 15+76, s)-Nets in Base 16

Best Known (15, 15+76, s)-Nets in Base 16

(15, 15+76, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 91, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 91, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(15, 15+76, 98)-Net over F₁₆ — Digital

Digital (15, 91, 98)-net over F₁₆, using

net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(15, 15+76, 745)-Net in Base 16 — Upper bound on s

There is no (15, 91, 746)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 39 158227 885948 661009 053074 897728 956434 679544 868865 677217 837973 978648 486443 099751 429169 203855 274272 803004 116396 > 16⁹¹ [i]