MinT - Best Known (101−79, 101, s)-Nets in Base 25

Best Known (101−79, 101, s)-Nets in Base 25

(101−79, 101, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 101, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 101, 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]

(101−79, 101, 171)-Net over F₂₅ — Digital

Digital (22, 101, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 101, 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]

(101−79, 101, 2443)-Net in Base 25 — Upper bound on s

There is no (22, 101, 2444)-net in base 25, because

1 times m-reduction [i] would yield (22, 100, 2444)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 62 613889 387380 489017 266374 702007 032303 552944 246521 719216 551658 719263 365340 494268 666197 110115 388803 456435 977322 160749 920728 375429 402667 851105 > 25¹⁰⁰ [i]