MinT - Best Known (71−27, 71, s)-Nets in Base 25

Best Known (71−27, 71, s)-Nets in Base 25

(71−27, 71, 288)-Net over F₂₅ — Constructive and digital

Digital (44, 71, 288)-net over F₂₅, using

t-expansion [i] based on digital (41, 71, 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]

(71−27, 71, 2901)-Net over F₂₅ — Digital

Digital (44, 71, 2901)-net over F₂₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(71−27, 71, 7953602)-Net in Base 25 — Upper bound on s

There is no (44, 71, 7953603)-net in base 25, because

1 times m-reduction [i] would yield (44, 70, 7953603)-net in base 25, but
- the generalized Rao bound for nets shows that 25^mÂ â‰¥ 71 746594 910217 623467 668808 204681 427075 408871 337816 175572 421060 098659 572304 573876 294658 582773 920425 > 25⁷⁰ [i]