MinT - Best Known (90−35, 90, s)-Nets in Base 5

Best Known (90−35, 90, s)-Nets in Base 5

(90−35, 90, 252)-Net over F₅ — Constructive and digital

Digital (55, 90, 252)-net over F₅, using

trace code for nets [i] based on digital (10, 45, 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]

(90−35, 90, 8176)-Net in Base 5 — Upper bound on s

There is no (55, 90, 8177)-net in base 5, because

1 times m-reduction [i] would yield (55, 89, 8177)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 161 843604 151405 253393 714464 063302 174008 748855 162776 371608 878725 > 5⁸⁹ [i]