MinT - Best Known (29, 29+75, s)-Nets in Base 25

Best Known (29, 29+75, s)-Nets in Base 25

(29, 29+75, 200)-Net over F₂₅ — Constructive and digital

Digital (29, 104, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 104, 200)-net over F₂₅, using
- net from sequence [i] based on digital (25, 199)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 25 and N(F) ≥ 200, using
    - a function field by GarcÃa and Quoos [i]

(29, 29+75, 4736)-Net in Base 25 — Upper bound on s

There is no (29, 104, 4737)-net in base 25, because

1 times m-reduction [i] would yield (29, 103, 4737)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 974532 691313 578548 695167 740537 629582 174500 651831 182889 581258 780199 835894 554015 270495 587058 969643 218018 747582 645801 381051 751264 549692 582744 274425 > 25¹⁰³ [i]