MinT - Best Known (106−84, 106, s)-Nets in Base 25

Best Known (106−84, 106, s)-Nets in Base 25

(106−84, 106, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 106, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 106, 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]

(106−84, 106, 171)-Net over F₂₅ — Digital

Digital (22, 106, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 106, 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]

(106−84, 106, 2299)-Net in Base 25 — Upper bound on s

There is no (22, 106, 2300)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 15452 425291 525344 670047 997751 270209 331430 031850 111130 549352 795848 823575 470140 816236 540284 391032 331565 180668 134968 404880 438724 267738 180975 396383 147969 > 25¹⁰⁶ [i]