MinT - Best Known (42, 42+41, s)-Nets in Base 25

Best Known (42, 42+41, s)-Nets in Base 25

(42, 42+41, 288)-Net over F₂₅ — Constructive and digital

Digital (42, 83, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 83, 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+41, 540)-Net over F₂₅ — Digital

Digital (42, 83, 540)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(42, 42+41, 186476)-Net in Base 25 — Upper bound on s

There is no (42, 83, 186477)-net in base 25, because

1 times m-reduction [i] would yield (42, 82, 186477)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 4 276485 340429 283485 247306 895155 012248 793298 406945 946910 045609 647363 468285 259324 273130 674857 848799 426676 349382 034145 > 25⁸² [i]