MinT - Best Known (89−72, 89, s)-Nets in Base 25

Best Known (89−72, 89, s)-Nets in Base 25

(89−72, 89, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 89, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 89, 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]

(89−72, 89, 150)-Net over F₂₅ — Digital

Digital (17, 89, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 89, 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]

(89−72, 89, 1681)-Net in Base 25 — Upper bound on s

There is no (17, 89, 1682)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 26423 269904 045153 380731 051836 985647 235060 221156 911344 269487 878817 213427 244435 012589 218872 456195 298860 309137 681334 943206 135105 > 25⁸⁹ [i]