MinT - Best Known (78−64, 78, s)-Nets in Base 16

Best Known (78−64, 78, s)-Nets in Base 16

(78−64, 78, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 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]

(78−64, 78, 97)-Net over F₁₆ — Digital

Digital (14, 78, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 78, 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]

(78−64, 78, 716)-Net in Base 16 — Upper bound on s

There is no (14, 78, 717)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 8453 101948 804296 661295 278834 768822 752757 520913 145324 393606 962513 669315 596161 373273 853545 694586 > 16⁷⁸ [i]