MinT - Best Known (109−85, 109, s)-Nets in Base 25

Best Known (109−85, 109, s)-Nets in Base 25

(109−85, 109, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 109, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 109, 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]

(109−85, 109, 184)-Net over F₂₅ — Digital

Digital (24, 109, 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]

(109−85, 109, 2683)-Net in Base 25 — Upper bound on s

There is no (24, 109, 2684)-net in base 25, because

1 times m-reduction [i] would yield (24, 108, 2684)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 9 558082 485577 727779 703297 680736 450593 691987 195961 541612 201486 869950 548946 472653 527424 616227 302531 864194 543988 558205 026553 572488 824749 547346 329118 711745 > 25¹⁰⁸ [i]