MinT - Best Known (38−27, 38, s)-Nets in Base 25

Best Known (38−27, 38, s)-Nets in Base 25

(38−27, 38, 126)-Net over F₂₅ — Constructive and digital

Digital (11, 38, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 38, 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]

(38−27, 38, 2242)-Net in Base 25 — Upper bound on s

There is no (11, 38, 2243)-net in base 25, because

1 times m-reduction [i] would yield (11, 37, 2243)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 5317 123991 231720 055371 702840 931208 906610 752963 416745 > 25³⁷ [i]