MinT - Best Known (40, 40+55, s)-Nets in Base 25

Best Known (40, 40+55, s)-Nets in Base 25

(40, 40+55, 208)-Net over F₂₅ — Constructive and digital

Digital (40, 95, 208)-net over F₂₅, using

t-expansion [i] based on digital (35, 95, 208)-net over F₂₅, using
- net from sequence [i] based on digital (35, 207)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 35 and N(F) ≥ 208, using
    - a function field by GarcÃa and Quoos [i]

(40, 40+55, 240)-Net over F₂₅ — Digital

Digital (40, 95, 240)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+55, 33489)-Net in Base 25 — Upper bound on s

There is no (40, 95, 33490)-net in base 25, because

1 times m-reduction [i] would yield (40, 94, 33490)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 254902 343048 467409 397604 699330 832419 877347 627282 179842 677079 828124 630034 018173 652250 956257 029609 604416 792527 835202 959201 898661 325521 > 25⁹⁴ [i]