MinT - Best Known (42, 42+65, s)-Nets in Base 25

Best Known (42, 42+65, s)-Nets in Base 25

(42, 42+65, 288)-Net over F₂₅ — Constructive and digital

Digital (42, 107, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 107, 288)-net over F₂₅, using
- net from sequence [i] based on digital (41, 287)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 41 and N(F) ≥ 288, using
    - a function field by GarcÃa and Quoos [i]

(42, 42+65, 22752)-Net in Base 25 — Upper bound on s

There is no (42, 107, 22753)-net in base 25, because

1 times m-reduction [i] would yield (42, 106, 22753)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 15209 030277 450825 395701 465526 280807 322141 548250 681680 297973 356095 586418 925403 836162 425486 092214 147120 838919 591729 927720 226016 898653 002976 803338 157825 > 25¹⁰⁶ [i]