MinT - Best Known (15, 64, s)-Nets in Base 25

Best Known (15, 64, s)-Nets in Base 25

(15, 64, 126)-Net over F₂₅ — Constructive and digital

Digital (15, 64, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 64, 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]

(15, 64, 140)-Net over F₂₅ — Digital

Digital (15, 64, 140)-net over F₂₅, using

net from sequence [i] based on digital (15, 139)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 15 and N(F) ≥ 140, using
  - an algebraic function field by Teo [i]

(15, 64, 1896)-Net in Base 25 — Upper bound on s

There is no (15, 64, 1897)-net in base 25, because

1 times m-reduction [i] would yield (15, 63, 1897)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 11866 795122 813485 956113 494990 996588 544296 974125 045805 461822 870378 199254 363332 806498 530625 > 25⁶³ [i]