MinT - Best Known (22, 22+81, s)-Nets in Base 25

Best Known (22, 22+81, s)-Nets in Base 25

(22, 22+81, 148)-Net over F₂₅ — Constructive and digital

Digital (22, 103, 148)-net over F₂₅, using

t-expansion [i] based on digital (19, 103, 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]

(22, 22+81, 171)-Net over F₂₅ — Digital

Digital (22, 103, 171)-net over F₂₅, using

t-expansion [i] based on digital (20, 103, 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]

(22, 22+81, 2390)-Net in Base 25 — Upper bound on s

There is no (22, 103, 2391)-net in base 25, because

1 times m-reduction [i] would yield (22, 102, 2391)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 39155 938946 741432 159826 585354 688525 857828 220926 296836 494351 383088 230210 269381 321506 814985 016160 035227 742665 380874 127326 347532 163683 992444 551745 > 25¹⁰² [i]