MinT - Best Known (140−66, 140, s)-Nets in Base 5

Best Known (140−66, 140, s)-Nets in Base 5

(140−66, 140, 132)-Net over F₅ — Constructive and digital

Digital (74, 140, 132)-net over F₅, using

trace code for nets [i] based on digital (4, 70, 66)-net over F₂₅, using
- net from sequence [i] based on digital (4, 65)-sequence over F₂₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 4 and N(F) ≥ 66, using
    - a function field by GarcÃa and Quoos [i]

(140−66, 140, 168)-Net over F₅ — Digital

Digital (74, 140, 168)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−66, 140, 3014)-Net in Base 5 — Upper bound on s

There is no (74, 140, 3015)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 72 487146 983498 110513 456406 094780 334568 728939 294617 934143 308662 380396 638795 291934 248494 946545 028765 > 5¹⁴⁰ [i]