MinT - Best Known (15, 15+71, s)-Nets in Base 25

Best Known (15, 15+71, s)-Nets in Base 25

(15, 15+71, 126)-Net over F₂₅ — Constructive and digital

Digital (15, 86, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 86, 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, 15+71, 140)-Net over F₂₅ — Digital

Digital (15, 86, 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, 15+71, 1420)-Net in Base 25 — Upper bound on s

There is no (15, 86, 1421)-net in base 25, because

1 times m-reduction [i] would yield (15, 85, 1421)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 67540 954097 934756 461191 351367 921541 683339 892796 234270 084087 611635 195750 051279 891749 980478 939953 323248 878552 537545 663209 > 25⁸⁵ [i]