MinT - Best Known (20, 20+23, s)-Nets in Base 25

Best Known (20, 20+23, s)-Nets in Base 25

(20, 20+23, 148)-Net over F₂₅ — Constructive and digital

Digital (20, 43, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 43, 148)-net over F₂₅, using
- net from sequence [i] based on digital (19, 147)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 19 and N(F) ≥ 148, using
    - a function field by GarcÃa and Quoos [i]

(20, 20+23, 215)-Net over F₂₅ — Digital

Digital (20, 43, 215)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(20, 20+23, 44497)-Net in Base 25 — Upper bound on s

There is no (20, 43, 44498)-net in base 25, because

1 times m-reduction [i] would yield (20, 42, 44498)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 51701 041773 060767 561743 569102 801401 700581 662893 004478 630353 > 25⁴² [i]