MinT - Best Known (66−24, 66, s)-Nets in Base 5

Best Known (66−24, 66, s)-Nets in Base 5

(66−24, 66, 208)-Net over F₅ — Constructive and digital

Digital (42, 66, 208)-net over F₅, using

trace code for nets [i] based on digital (9, 33, 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]

(66−24, 66, 250)-Net over F₅ — Digital

Digital (42, 66, 250)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(66−24, 66, 9230)-Net in Base 5 — Upper bound on s

There is no (42, 66, 9231)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 13556 979748 240551 696078 292249 473852 951118 403025 > 5⁶⁶ [i]