MinT - Best Known (24, 24+81, s)-Nets in Base 25

Best Known (24, 24+81, s)-Nets in Base 25

(24, 24+81, 148)-Net over F₂₅ — Constructive and digital

Digital (24, 105, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 105, 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]

(24, 24+81, 184)-Net over F₂₅ — Digital

Digital (24, 105, 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]

(24, 24+81, 2811)-Net in Base 25 — Upper bound on s

There is no (24, 105, 2812)-net in base 25, because

1 times m-reduction [i] would yield (24, 104, 2812)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 24 404641 408891 838288 452813 127044 845643 578162 956700 134725 269373 590548 375858 095144 242224 556490 845389 739165 484189 216200 389050 145380 762053 520108 057345 > 25¹⁰⁴ [i]