MinT - Best Known (12, 37, s)-Nets in Base 25

Best Known (12, 37, s)-Nets in Base 25

(12, 37, 126)-Net over F₂₅ — Constructive and digital

Digital (12, 37, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 37, 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]

(12, 37, 3437)-Net in Base 25 — Upper bound on s

There is no (12, 37, 3438)-net in base 25, because

1 times m-reduction [i] would yield (12, 36, 3438)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 212 300870 320303 195601 384116 303706 272205 066069 605441 > 25³⁶ [i]