MinT - Best Known (9, 62, s)-Nets in Base 16

Best Known (9, 62, s)-Nets in Base 16

(9, 62, 65)-Net over F₁₆ — Constructive and digital

Digital (9, 62, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 62, 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, 62, 72)-Net over F₁₆ — Digital

Digital (9, 62, 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, 62, 456)-Net in Base 16 — Upper bound on s

There is no (9, 62, 457)-net in base 16, because

1 times m-reduction [i] would yield (9, 61, 457)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 29 806131 810879 548955 365141 972866 485624 594032 333861 044687 052861 245819 653856 > 16⁶¹ [i]