MinT - Best Known (18, 18+78, s)-Nets in Base 25

Best Known (18, 18+78, s)-Nets in Base 25

(18, 18+78, 126)-Net over F₂₅ — Constructive and digital

Digital (18, 96, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 96, 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+78, 153)-Net over F₂₅ — Digital

Digital (18, 96, 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+78, 1750)-Net in Base 25 — Upper bound on s

There is no (18, 96, 1751)-net in base 25, because

the generalized Rao bound for nets shows that 25^mÂ â‰¥ 160 191510 789968 852672 631085 356762 538830 636955 940815 442178 798998 330478 146893 114432 579836 465431 982120 854880 012488 713498 699677 284218 233625 > 25⁹⁶ [i]