MinT - Best Known (87−73, 87, s)-Nets in Base 25

Best Known (87−73, 87, s)-Nets in Base 25

(87−73, 87, 126)-Net over F₂₅ — Constructive and digital

Digital (14, 87, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 87, 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]

(87−73, 87, 130)-Net over F₂₅ — Digital

Digital (14, 87, 130)-net over F₂₅, using

net from sequence [i] based on digital (14, 129)-sequence over F₂₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 14 and N(F) ≥ 130, using
  - an algebraic function field by Teo [i]

(87−73, 87, 1281)-Net in Base 25 — Upper bound on s

There is no (14, 87, 1282)-net in base 25, because

1 times m-reduction [i] would yield (14, 86, 1282)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1 699431 005676 449329 833905 987198 379785 474233 566351 611175 186356 576937 946085 422553 574231 238860 544007 582524 023530 461858 722625 > 25⁸⁶ [i]