MinT - Best Known (71−57, 71, s)-Nets in Base 16

Best Known (71−57, 71, s)-Nets in Base 16

(71−57, 71, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 71, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 71, 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]

(71−57, 71, 97)-Net over F₁₆ — Digital

Digital (14, 71, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 71, 97)-net over F₁₆, using
- net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(71−57, 71, 755)-Net in Base 16 — Upper bound on s

There is no (14, 71, 756)-net in base 16, because

1 times m-reduction [i] would yield (14, 70, 756)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 943163 333253 575156 332227 810090 166792 205665 548897 001818 213174 095762 442700 716372 870696 > 16⁷⁰ [i]