MinT - Best Known (19, 19+69, s)-Nets in Base 16

Best Known (19, 19+69, s)-Nets in Base 16

(19, 19+69, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 88, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 88, 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]

(19, 19+69, 129)-Net over F₁₆ — Digital

Digital (19, 88, 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]

(19, 19+69, 1069)-Net in Base 16 — Upper bound on s

There is no (19, 88, 1070)-net in base 16, because

1 times m-reduction [i] would yield (19, 87, 1070)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 591 059053 981020 500227 366273 649651 188071 349798 719573 402996 583156 974006 149557 499395 574595 692910 856039 292326 > 16⁸⁷ [i]