MinT - Best Known (112, 142, s)-Nets in Base 5

Best Known (112, 142, s)-Nets in Base 5

(112, 142, 576)-Net over F₅ — Constructive and digital

Digital (112, 142, 576)-net over F₅, using

trace code for nets [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]

(112, 142, 7734)-Net over F₅ — Digital

Digital (112, 142, 7734)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 142, 6646943)-Net in Base 5 — Upper bound on s

There is no (112, 142, 6646944)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 1793 664004 806596 011534 613533 902272 061541 995792 143516 009231 768704 454100 821432 275343 851810 879731 192449 > 5¹⁴² [i]