MinT - Best Known (19, 19+77, s)-Nets in Base 16

Best Known (19, 19+77, s)-Nets in Base 16

(19, 19+77, 65)-Net over F₁₆ — Constructive and digital

Digital (19, 96, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 96, 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+77, 129)-Net over F₁₆ — Digital

Digital (19, 96, 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+77, 1004)-Net in Base 16 — Upper bound on s

There is no (19, 96, 1005)-net in base 16, because

1 times m-reduction [i] would yield (19, 95, 1005)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 485232 124805 889444 529305 185922 162443 380155 253306 542789 910736 235280 787562 481819 768620 456888 889505 108647 096808 085476 > 16⁹⁵ [i]