MinT - Best Known (88−71, 88, s)-Nets in Base 25

Best Known (88−71, 88, s)-Nets in Base 25

(88−71, 88, 126)-Net over F₂₅ — Constructive and digital

Digital (17, 88, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 88, 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]

(88−71, 88, 150)-Net over F₂₅ — Digital

Digital (17, 88, 150)-net over F₂₅, using

t-expansion [i] based on digital (16, 88, 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]

(88−71, 88, 1711)-Net in Base 25 — Upper bound on s

There is no (17, 88, 1712)-net in base 25, because

1 times m-reduction [i] would yield (17, 87, 1712)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 42 502243 345996 032734 717832 549934 029760 103627 222045 095771 646727 318165 983822 174062 641309 889175 014343 018916 105969 511300 342657 > 25⁸⁷ [i]