MinT - Best Known (70−26, 70, s)-Nets in Base 25

Best Known (70−26, 70, s)-Nets in Base 25

(70−26, 70, 304)-Net over F₂₅ — Constructive and digital

Digital (44, 70, 304)-net over F₂₅, using

generalized (u,Â u+v)-construction [i] based on
1. digital (3, 11, 52)-net over F₂₅, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by GarcÃa and Quoos [i]
2. digital (10, 23, 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]
3. digital (10, 36, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(70−26, 70, 3493)-Net over F₂₅ — Digital

Digital (44, 70, 3493)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70−26, 70, 7953602)-Net in Base 25 — Upper bound on s

There is no (44, 70, 7953603)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 71 746594 910217 623467 668808 204681 427075 408871 337816 175572 421060 098659 572304 573876 294658 582773 920425 > 25⁷⁰ [i]