MinT - Best Known (13, 52, s)-Nets in Base 25

Best Known (13, 52, s)-Nets in Base 25

(13, 52, 126)-Net over F₂₅ — Constructive and digital

Digital (13, 52, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 52, 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]

(13, 52, 1858)-Net in Base 25 — Upper bound on s

There is no (13, 52, 1859)-net in base 25, because

1 times m-reduction [i] would yield (13, 51, 1859)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 198848 783642 557094 265367 349524 921349 773379 900623 457904 341843 627729 188825 > 25⁵¹ [i]