MinT - Best Known (182−74, 182, s)-Nets in Base 3

Best Known (182−74, 182, s)-Nets in Base 3

(182−74, 182, 148)-Net over F₃ — Constructive and digital

Digital (108, 182, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 91, 74)-net over F₉, using
- net from sequence [i] based on digital (17, 73)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
    - a function field by GarcÃa and Quoos [i]

(182−74, 182, 164)-Net over F₃ — Digital

Digital (108, 182, 164)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−74, 182, 1592)-Net in Base 3 — Upper bound on s

There is no (108, 182, 1593)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 695 117186 372848 272674 480295 103366 516648 612276 369529 264651 824103 758957 944762 630178 652771 > 3¹⁸² [i]