MinT - Best Known (40, 40+43, s)-Nets in Base 25

Best Known (40, 40+43, s)-Nets in Base 25

(40, 40+43, 230)-Net over F₂₅ — Constructive and digital

Digital (40, 83, 230)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (9, 30, 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, 53, 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]

(40, 40+43, 403)-Net over F₂₅ — Digital

Digital (40, 83, 403)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+43, 103958)-Net in Base 25 — Upper bound on s

There is no (40, 83, 103959)-net in base 25, because

1 times m-reduction [i] would yield (40, 82, 103959)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4 277106 847944 962282 745462 719222 630176 265650 879058 433762 767564 036107 435201 503565 847030 003307 579349 677156 799150 593865 > 25⁸² [i]