MinT - Best Known (17, 17+89, s)-Nets in Base 25

Best Known (17, 17+89, s)-Nets in Base 25

(17, 17+89, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 106, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 106, 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+89, 150)-Net over F₂₅ — Digital

Digital (17, 106, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 106, 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+89, 1535)-Net in Base 25 — Upper bound on s

There is no (17, 106, 1536)-net in base 25, because

1 times m-reduction [i] would yield (17, 105, 1536)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 620 949636 422116 293162 679613 625870 988657 078505 010238 942578 165526 981013 218660 393136 085623 056910 127651 624433 281028 918799 179101 581305 944341 096240 922625 > 25¹⁰⁵ [i]