MinT - Best Known (17, 17+71, s)-Nets in Base 16

Best Known (17, 17+71, s)-Nets in Base 16

(17, 17+71, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 88, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 88, 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+71, 112)-Net over F₁₆ — Digital

Digital (17, 88, 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+71, 893)-Net in Base 16 — Upper bound on s

There is no (17, 88, 894)-net in base 16, because

1 times m-reduction [i] would yield (17, 87, 894)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 587 891182 568309 259300 904382 706956 267782 815934 319819 438769 283158 209556 005753 257992 483275 973280 640096 646226 > 16⁸⁷ [i]