MinT - Best Known (90−36, 90, s)-Nets in Base 5

Best Known (90−36, 90, s)-Nets in Base 5

(90−36, 90, 208)-Net over F₅ — Constructive and digital

Digital (54, 90, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 45, 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]

(90−36, 90, 210)-Net over F₅ — Digital

Digital (54, 90, 210)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(90−36, 90, 5887)-Net in Base 5 — Upper bound on s

There is no (54, 90, 5888)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 807 953090 804260 535772 687623 155357 287099 991784 924377 331709 210625 > 5⁹⁰ [i]