MinT - Best Known (75−58, 75, s)-Nets in Base 16

Best Known (75−58, 75, s)-Nets in Base 16

(75−58, 75, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 75, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 75, 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]

(75−58, 75, 112)-Net over F₁₆ — Digital

Digital (17, 75, 112)-net over F₁₆, using

net from sequence [i] based on digital (17, 111)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 17 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(75−58, 75, 996)-Net in Base 16 — Upper bound on s

There is no (17, 75, 997)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 094942 712427 994548 565731 551254 481946 535538 643287 177810 490374 405108 940649 226280 182419 750496 > 16⁷⁵ [i]