MinT - Best Known (18, 18+72, s)-Nets in Base 25

Best Known (18, 18+72, s)-Nets in Base 25

(18, 18+72, 126)-Net over F₂₅ — Constructive and digital

Digital (18, 90, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 90, 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]

(18, 18+72, 153)-Net over F₂₅ — Digital

Digital (18, 90, 153)-net over F₂₅, using

net from sequence [i] based on digital (18, 152)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 18 and N(F) ≥ 153, using
  - an algebraic function field by Teo [i]

(18, 18+72, 1840)-Net in Base 25 — Upper bound on s

There is no (18, 90, 1841)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 659430 332192 389887 275683 008855 437860 637815 206148 752917 805439 350453 534742 575558 885365 776674 248753 333506 212218 512673 320324 702945 > 25⁹⁰ [i]