MinT - Best Known (98−81, 98, s)-Nets in Base 25

Best Known (98−81, 98, s)-Nets in Base 25

(98−81, 98, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 98, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 98, 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]

(98−81, 98, 150)-Net over F₂₅ — Digital

Digital (17, 98, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 98, 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]

(98−81, 98, 1591)-Net in Base 25 — Upper bound on s

There is no (17, 98, 1592)-net in base 25, because

1 times m-reduction [i] would yield (17, 97, 1592)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4011 486069 946635 700617 340801 792009 921174 560373 900486 723922 744449 875852 736634 627438 184199 549261 519397 872592 333553 048838 917355 504479 462913 > 25⁹⁷ [i]