MinT - Best Known (98−75, 98, s)-Nets in Base 16

Best Known (98−75, 98, s)-Nets in Base 16

(98−75, 98, 65)-Net over F₁₆ — Constructive and digital

Digital (23, 98, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 98, 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]

(98−75, 98, 129)-Net over F₁₆ — Digital

Digital (23, 98, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 98, 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]

(98−75, 98, 1381)-Net in Base 16 — Upper bound on s

There is no (23, 98, 1382)-net in base 16, because

1 times m-reduction [i] would yield (23, 97, 1382)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 646 866914 181680 631767 097278 259364 364304 529937 122621 431816 789361 964950 955739 442103 664665 330661 103630 018107 918999 451561 > 16⁹⁷ [i]