MinT - Best Known (17, 17+97, s)-Nets in Base 16

Best Known (17, 17+97, s)-Nets in Base 16

(17, 17+97, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 114, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 114, 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+97, 112)-Net over F₁₆ — Digital

Digital (17, 114, 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+97, 827)-Net in Base 16 — Upper bound on s

There is no (17, 114, 828)-net in base 16, because

1 times m-reduction [i] would yield (17, 113, 828)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12037 759207 683384 204481 385042 926330 876297 792592 928941 991754 273255 638969 315174 893667 288967 671166 709202 299596 403251 087025 404915 324483 875211 > 16¹¹³ [i]