MinT - Best Known (109−96, 109, s)-Nets in Base 25

Best Known (109−96, 109, s)-Nets in Base 25

(109−96, 109, 126)-Net over F₂₅ — Constructive and digital

Digital (13, 109, 126)-net over F₂₅, using

t-expansion [i] based on digital (10, 109, 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]

(109−96, 109, 1139)-Net in Base 25 — Upper bound on s

There is no (13, 109, 1140)-net in base 25, because

4 times m-reduction [i] would yield (13, 105, 1140)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 614 020209 951601 302516 032181 948232 003194 345415 655080 138994 483444 220836 822600 271887 201370 295172 789244 738572 394246 261193 701548 856344 616973 292625 253825 > 25¹⁰⁵ [i]