MinT - Best Known (43, 90, s)-Nets in Base 25

Best Known (43, 90, s)-Nets in Base 25

(43, 90, 288)-Net over F₂₅ — Constructive and digital

Digital (43, 90, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 90, 288)-net over F₂₅, using
- net from sequence [i] based on digital (41, 287)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288, using
    - a function field by GarcÃa and Quoos [i]

(43, 90, 408)-Net over F₂₅ — Digital

Digital (43, 90, 408)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 90, 100835)-Net in Base 25 — Upper bound on s

There is no (43, 90, 100836)-net in base 25, because

1 times m-reduction [i] would yield (43, 89, 100836)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 26104 034605 060141 288130 085548 112238 932033 160036 289519 835404 811408 641323 478136 714018 110003 466657 378741 769488 357792 476098 696225 > 25⁸⁹ [i]