MinT - Best Known (56−33, 56, s)-Nets in Base 25

Best Known (56−33, 56, s)-Nets in Base 25

(56−33, 56, 148)-Net over F₂₅ — Constructive and digital

Digital (23, 56, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 56, 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]

(56−33, 56, 176)-Net over F₂₅ — Digital

Digital (23, 56, 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]

(56−33, 56, 18094)-Net in Base 25 — Upper bound on s

There is no (23, 56, 18095)-net in base 25, because

1 times m-reduction [i] would yield (23, 55, 18095)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 77060 661745 662768 422153 150359 712950 169773 465994 945745 216805 047767 405800 076929 > 25⁵⁵ [i]