MinT - Best Known (32, 69, s)-Nets in Base 25

Best Known (32, 69, s)-Nets in Base 25

(32, 69, 204)-Net over F₂₅ — Constructive and digital

Digital (32, 69, 204)-net over F₂₅, using

t-expansion [i] based on digital (30, 69, 204)-net over F₂₅, using
- net from sequence [i] based on digital (30, 203)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 30 and N(F) ≥ 204, using
    - a function field by GarcÃa and Quoos [i]

(32, 69, 287)-Net over F₂₅ — Digital

Digital (32, 69, 287)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(32, 69, 60111)-Net in Base 25 — Upper bound on s

There is no (32, 69, 60112)-net in base 25, because

1 times m-reduction [i] would yield (32, 68, 60112)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 114806 192825 995188 993102 956366 602353 270294 391334 392852 382693 668887 739212 623139 355634 634266 605825 > 25⁶⁸ [i]