MinT - Best Known (29, 102, s)-Nets in Base 25

Best Known (29, 102, s)-Nets in Base 25

(29, 102, 200)-Net over F₂₅ — Constructive and digital

Digital (29, 102, 200)-net over F₂₅, using

t-expansion [i] based on digital (25, 102, 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, 102, 4952)-Net in Base 25 — Upper bound on s

There is no (29, 102, 4953)-net in base 25, because

1 times m-reduction [i] would yield (29, 101, 4953)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 1556 461900 602411 864579 025482 221493 431771 846609 173263 881116 560938 744253 609725 249458 252293 148809 887112 862346 930173 588928 276682 046619 668954 059745 > 25¹⁰¹ [i]