MinT - Best Known (107−83, 107, s)-Nets in Base 25

Best Known (107−83, 107, s)-Nets in Base 25

(107−83, 107, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 107, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 107, 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]

(107−83, 107, 184)-Net over F₂₅ — Digital

Digital (24, 107, 184)-net over F₂₅, using

net from sequence [i] based on digital (24, 183)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 24 and N(F) ≥ 184, using
  - an algebraic function field by Teo [i]

(107−83, 107, 2744)-Net in Base 25 — Upper bound on s

There is no (24, 107, 2745)-net in base 25, because

1 times m-reduction [i] would yield (24, 106, 2745)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 15292 739241 779950 198093 637943 992712 909835 628236 717356 365815 381400 073254 264144 744465 512103 494415 334048 974017 274874 609638 731909 469358 084346 795862 820889 > 25¹⁰⁶ [i]