MinT - Best Known (87−66, 87, s)-Nets in Base 25

Best Known (87−66, 87, s)-Nets in Base 25

(87−66, 87, 148)-Net over F₂₅ — Constructive and digital

Digital (21, 87, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 87, 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]

(87−66, 87, 171)-Net over F₂₅ — Digital

Digital (21, 87, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 87, 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]

(87−66, 87, 2641)-Net in Base 25 — Upper bound on s

There is no (21, 87, 2642)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 42 254539 581340 750356 153423 190081 740836 945598 370055 950195 086802 872169 540651 867912 838053 019188 624878 592975 960306 520923 503025 > 25⁸⁷ [i]