MinT - Best Known (65−43, 65, s)-Nets in Base 25

Best Known (65−43, 65, s)-Nets in Base 25

(65−43, 65, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 65, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 65, 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]

(65−43, 65, 171)-Net over F₂₅ — Digital

Digital (22, 65, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 65, 171)-net over F₂₅, using
- net from sequence [i] based on digital (20, 170)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 20 and N(F) ≥ 171, using
    - an algebraic function field by Teo [i]

(65−43, 65, 6575)-Net in Base 25 — Upper bound on s

There is no (22, 65, 6576)-net in base 25, because

1 times m-reduction [i] would yield (22, 64, 6576)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 294004 688097 906803 005899 425614 744500 335268 695621 225682 272622 203455 613769 306475 092718 583425 > 25⁶⁴ [i]