MinT - Best Known (22, 22+67, s)-Nets in Base 16

Best Known (22, 22+67, s)-Nets in Base 16

(22, 22+67, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 89, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 89, 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]

(22, 22+67, 129)-Net over F₁₆ — Digital

Digital (22, 89, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 89, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(22, 22+67, 1408)-Net in Base 16 — Upper bound on s

There is no (22, 89, 1409)-net in base 16, because

1 times m-reduction [i] would yield (22, 88, 1409)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9327 053010 370399 453874 319958 032994 969009 110524 566201 319224 063547 074563 613115 056886 589297 537185 993764 843456 > 16⁸⁸ [i]