MinT - Best Known (53−29, 53, s)-Nets in Base 25

Best Known (53−29, 53, s)-Nets in Base 25

(53−29, 53, 152)-Net over F₂₅ — Constructive and digital

Digital (24, 53, 152)-net over F₂₅, using

(u,Â u+v)-construction [i] based on
1. digital (0, 14, 26)-net over F₂₅, using
  - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
      - the rational function field F₂₅(x) [i]
    - Niederreiter sequence [i]
2. digital (10, 39, 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]

(53−29, 53, 213)-Net over F₂₅ — Digital

Digital (24, 53, 213)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(53−29, 53, 39220)-Net in Base 25 — Upper bound on s

There is no (24, 53, 39221)-net in base 25, because

1 times m-reduction [i] would yield (24, 52, 39221)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4 930696 068798 828584 761013 594550 202615 922857 105828 883816 515523 114005 131985 > 25⁵² [i]