MinT - Best Known (17, 17+77, s)-Nets in Base 16

Best Known (17, 17+77, s)-Nets in Base 16

(17, 17+77, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 94, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 94, 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]

(17, 17+77, 112)-Net over F₁₆ — Digital

Digital (17, 94, 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]

(17, 17+77, 865)-Net in Base 16 — Upper bound on s

There is no (17, 94, 866)-net in base 16, because

1 times m-reduction [i] would yield (17, 93, 866)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9825 864319 702124 943744 582670 588151 662530 214849 538750 826391 365743 724039 082794 722504 317748 105728 250295 228892 091296 > 16⁹³ [i]