MinT - Best Known (99−79, 99, s)-Nets in Base 16

Best Known (99−79, 99, s)-Nets in Base 16

(99−79, 99, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 99, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 99, 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]

(99−79, 99, 129)-Net over F₁₆ — Digital

Digital (20, 99, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 99, 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]

(99−79, 99, 1067)-Net in Base 16 — Upper bound on s

There is no (20, 99, 1068)-net in base 16, because

1 times m-reduction [i] would yield (20, 98, 1068)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10226 915538 086469 883926 194851 576328 192746 450594 587708 587733 191661 041583 811462 374379 496516 495052 195113 563770 019026 361006 > 16⁹⁸ [i]