MinT - Best Known (94−79, 94, s)-Nets in Base 16

Best Known (94−79, 94, s)-Nets in Base 16

(94−79, 94, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 94, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 94, 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]

(94−79, 94, 98)-Net over F₁₆ — Digital

Digital (15, 94, 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]

(94−79, 94, 741)-Net in Base 16 — Upper bound on s

There is no (15, 94, 742)-net in base 16, because

1 times m-reduction [i] would yield (15, 93, 742)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9691 720857 147794 642487 387490 413663 357788 861591 677691 496263 013339 529005 335541 840108 981424 961555 276161 760285 934496 > 16⁹³ [i]