MinT - Best Known (68−54, 68, s)-Nets in Base 16

Best Known (68−54, 68, s)-Nets in Base 16

(68−54, 68, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 68, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 68, 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]

(68−54, 68, 97)-Net over F₁₆ — Digital

Digital (14, 68, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 68, 97)-net over F₁₆, using
- net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(68−54, 68, 770)-Net in Base 16 — Upper bound on s

There is no (14, 68, 771)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 7759 992684 985812 137484 242227 739931 711586 480920 702963 337980 087180 067690 298219 289856 > 16⁶⁸ [i]