MinT - Best Known (40−27, 40, s)-Nets in Base 25

Best Known (40−27, 40, s)-Nets in Base 25

(40−27, 40, 126)-Net over F₂₅ — Constructive and digital

Digital (13, 40, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 40, 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]

(40−27, 40, 3683)-Net in Base 25 — Upper bound on s

There is no (13, 40, 3684)-net in base 25, because

1 times m-reduction [i] would yield (13, 39, 3684)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 3 316141 017460 456317 159710 738422 480425 387241 163604 536545 > 25³⁹ [i]