MinT - Best Known (78−58, 78, s)-Nets in Base 16

Best Known (78−58, 78, s)-Nets in Base 16

(78−58, 78, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 78, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 78, 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]

(78−58, 78, 129)-Net over F₁₆ — Digital

Digital (20, 78, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 78, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(78−58, 78, 1332)-Net in Base 16 — Upper bound on s

There is no (20, 78, 1333)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 8499 457201 371210 388503 827343 570534 906140 319694 001235 525296 785770 964334 548736 809209 520300 783456 > 16⁷⁸ [i]