MinT - Best Known (9, 9+26, s)-Nets in Base 16

Best Known (9, 9+26, s)-Nets in Base 16

(9, 9+26, 65)-Net over F₁₆ — Constructive and digital

Digital (9, 35, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 35, 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]

(9, 9+26, 72)-Net over F₁₆ — Digital

Digital (9, 35, 72)-net over F₁₆, using

net from sequence [i] based on digital (9, 71)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 9 and N(F) ≥ 72, using
  - a curve from the manYPoints database [i]

(9, 9+26, 652)-Net in Base 16 — Upper bound on s

There is no (9, 35, 653)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 404993 403709 036169 009693 183444 775395 405136 > 16³⁵ [i]