MinT - Best Known (18, 18+90, s)-Nets in Base 25

Best Known (18, 18+90, s)-Nets in Base 25

(18, 18+90, 126)-Net over F₂₅ — Constructive and digital

Digital (18, 108, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 108, 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+90, 153)-Net over F₂₅ — Digital

Digital (18, 108, 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+90, 1639)-Net in Base 25 — Upper bound on s

There is no (18, 108, 1640)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 9 576998 898909 846082 937298 825872 366162 574891 348844 879790 319039 457174 214578 088059 348520 621855 599104 337712 514477 722678 125333 127277 788630 155514 212949 241025 > 25¹⁰⁸ [i]