MinT - Best Known (74−51, 74, s)-Nets in Base 25

Best Known (74−51, 74, s)-Nets in Base 25

(74−51, 74, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 74, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 74, 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]

(74−51, 74, 176)-Net over F₂₅ — Digital

Digital (23, 74, 176)-net over F₂₅, using

net from sequence [i] based on digital (23, 175)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 23 and N(F) ≥ 176, using
  - an algebraic function field by Teo [i]

(74−51, 74, 5108)-Net in Base 25 — Upper bound on s

There is no (23, 74, 5109)-net in base 25, because

1 times m-reduction [i] would yield (23, 73, 5109)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 123820 370579 600399 929442 873889 172727 190881 093140 762701 005753 727449 319005 625739 458439 124336 859791 180601 > 25⁷³ [i]