MinT - Best Known (78−62, 78, s)-Nets in Base 16

Best Known (78−62, 78, s)-Nets in Base 16

(78−62, 78, 65)-Net over F₁₆ — Constructive and digital

Digital (16, 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]

(78−62, 78, 98)-Net over F₁₆ — Digital

Digital (16, 78, 98)-net over F₁₆, using

t-expansion [i] based on digital (15, 78, 98)-net over F₁₆, using
- net from sequence [i] based on digital (15, 97)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 15 and N(F) ≥ 98, using
    - a curve from the manYPoints database [i]

(78−62, 78, 869)-Net in Base 16 — Upper bound on s

There is no (16, 78, 870)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 8495 870817 005914 366809 091588 915219 506716 302035 534378 320398 565912 502403 927972 176320 101079 360176 > 16⁷⁸ [i]