MinT - Best Known (83−61, 83, s)-Nets in Base 25

Best Known (83−61, 83, s)-Nets in Base 25

(83−61, 83, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 83, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 83, 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]

(83−61, 83, 171)-Net over F₂₅ — Digital

Digital (22, 83, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 83, 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]

(83−61, 83, 3307)-Net in Base 25 — Upper bound on s

There is no (22, 83, 3308)-net in base 25, because

1 times m-reduction [i] would yield (22, 82, 3308)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4 280172 868568 900824 586569 101131 814415 692141 049656 022649 758492 917366 382385 145476 521204 892225 677636 145278 477155 963457 > 25⁸² [i]