MinT - Best Known (48−37, 48, s)-Nets in Base 25

Best Known (48−37, 48, s)-Nets in Base 25

(48−37, 48, 126)-Net over F₂₅ — Constructive and digital

Digital (11, 48, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 48, 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]

(48−37, 48, 1397)-Net in Base 25 — Upper bound on s

There is no (11, 48, 1398)-net in base 25, because

1 times m-reduction [i] would yield (11, 47, 1398)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 510581 093498 904437 625891 703375 965460 286065 302181 017581 118043 335265 > 25⁴⁷ [i]