MinT - Best Known (70−55, 70, s)-Nets in Base 16

Best Known (70−55, 70, s)-Nets in Base 16

(70−55, 70, 65)-Net over F₁₆ — Constructive and digital

Digital (15, 70, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 70, 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]

(70−55, 70, 98)-Net over F₁₆ — Digital

Digital (15, 70, 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]

(70−55, 70, 855)-Net in Base 16 — Upper bound on s

There is no (15, 70, 856)-net in base 16, because

1 times m-reduction [i] would yield (15, 69, 856)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 124287 528180 978925 963209 410296 505653 908851 331992 591696 779329 341672 894937 085889 057656 > 16⁶⁹ [i]