MinT - Best Known (34, 34+26, s)-Nets in Base 25

Best Known (34, 34+26, s)-Nets in Base 25

(34, 34+26, 252)-Net over F₂₅ — Constructive and digital

Digital (34, 60, 252)-net over F₂₅, using

2 times m-reduction [i] based on digital (34, 62, 252)-net over F₂₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (10, 24, 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]
  2. digital (10, 38, 126)-net over F₂₅, using
    - net from sequence [i] based on digital (10, 125)-sequence over F₂₅ (see above)

(34, 34+26, 973)-Net over F₂₅ — Digital

Digital (34, 60, 973)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(34, 34+26, 668684)-Net in Base 25 — Upper bound on s

There is no (34, 60, 668685)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 752318 277764 823918 168030 531690 209507 981112 983236 019046 580292 763489 725649 318651 977305 > 25⁶⁰ [i]