MinT - Best Known (17, 17+83, s)-Nets in Base 25

Best Known (17, 17+83, s)-Nets in Base 25

(17, 17+83, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 100, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 100, 126)-net over F₂₅, using
- net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
    - the Hermitian function field over F₂₅ [i]

(17, 17+83, 150)-Net over F₂₅ — Digital

Digital (17, 100, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 100, 150)-net over F₂₅, using
- net from sequence [i] based on digital (16, 149)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 16 and N(F) ≥ 150, using
    - an algebraic function field by Teo [i]

(17, 17+83, 1575)-Net in Base 25 — Upper bound on s

There is no (17, 100, 1576)-net in base 25, because

1 times m-reduction [i] would yield (17, 99, 1576)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 2 552084 654500 088892 619337 117286 263829 590498 582141 245844 877724 883290 148877 649006 692393 908836 668832 365149 861232 386226 180893 542406 988685 209025 > 25⁹⁹ [i]