MinT - Best Known (20, 20+88, s)-Nets in Base 25

Best Known (20, 20+88, s)-Nets in Base 25

(20, 20+88, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 108, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 108, 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]

(20, 20+88, 171)-Net over F₂₅ — Digital

Digital (20, 108, 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]

(20, 20+88, 1917)-Net in Base 25 — Upper bound on s

There is no (20, 108, 1918)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 9 560592 280967 643939 088090 091442 275943 099361 771349 532279 166813 800591 726036 785612 276380 759218 050820 257195 838222 596336 561133 315147 101755 072055 438550 210625 > 25¹⁰⁸ [i]