MinT - Best Known (67−50, 67, s)-Nets in Base 16

Best Known (67−50, 67, s)-Nets in Base 16

(67−50, 67, 65)-Net over F₁₆ — Constructive and digital

Digital (17, 67, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 67, 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]

(67−50, 67, 112)-Net over F₁₆ — Digital

Digital (17, 67, 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]

(67−50, 67, 1130)-Net in Base 16 — Upper bound on s

There is no (17, 67, 1131)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 476 673253 427239 774197 199651 345275 136019 031217 769257 235405 149143 019816 290898 447876 > 16⁶⁷ [i]