MinT - Best Known (62−22, 62, s)-Nets in Base 5

Best Known (62−22, 62, s)-Nets in Base 5

(62−22, 62, 208)-Net over F₅ — Constructive and digital

Digital (40, 62, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 31, 104)-net over F₂₅, using
- net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
    - a function field by GarcÃa and Quoos [i]

(62−22, 62, 262)-Net over F₅ — Digital

Digital (40, 62, 262)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(62−22, 62, 10673)-Net in Base 5 — Upper bound on s

There is no (40, 62, 10674)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 21 705498 310658 553613 335091 837236 703896 092777 > 5⁶² [i]