MinT - Best Known (30, 30+22, s)-Nets in Base 25

Best Known (30, 30+22, s)-Nets in Base 25

(30, 30+22, 230)-Net over F₂₅ — Constructive and digital

Digital (30, 52, 230)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (9, 20, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]
2. digital (10, 32, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(30, 30+22, 1057)-Net over F₂₅ — Digital

Digital (30, 52, 1057)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(30, 30+22, 830316)-Net in Base 25 — Upper bound on s

There is no (30, 52, 830317)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4 930404 749684 250584 871620 508383 224685 814470 495551 761084 546400 774698 886057 > 25⁵² [i]