MinT - Best Known (96−79, 96, s)-Nets in Base 25

Best Known (96−79, 96, s)-Nets in Base 25

(96−79, 96, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 96, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 96, 126)-net over F₂₅, using
- net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]

(96−79, 96, 150)-Net over F₂₅ — Digital

Digital (17, 96, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 96, 150)-net over F₂₅, using
- net from sequence [i] based on digital (16, 149)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 16 and N(F) ≥ 150, using
    - an algebraic function field by Teo [i]

(96−79, 96, 1610)-Net in Base 25 — Upper bound on s

There is no (17, 96, 1611)-net in base 25, because

1 times m-reduction [i] would yield (17, 95, 1611)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 6 460127 736343 296098 607511 882011 163148 216976 975691 691285 469425 933740 720260 102269 580968 006986 886041 573822 339197 003755 773614 209992 432825 > 25⁹⁵ [i]