MinT - Best Known (96−75, 96, s)-Nets in Base 25

Best Known (96−75, 96, s)-Nets in Base 25

(96−75, 96, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 96, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 96, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(96−75, 96, 171)-Net over F₂₅ — Digital

Digital (21, 96, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 96, 171)-net over F₂₅, using
- net from sequence [i] based on digital (20, 170)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 20 and N(F) ≥ 171, using
    - an algebraic function field by Teo [i]

(96−75, 96, 2351)-Net in Base 25 — Upper bound on s

There is no (21, 96, 2352)-net in base 25, because

1 times m-reduction [i] would yield (21, 95, 2352)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 6 382225 660369 924135 995562 840004 391379 457557 587525 963036 882994 181658 389513 130117 809884 202533 988956 038280 680193 219640 073858 437886 532225 > 25⁹⁵ [i]