MinT - Best Known (166−66, 166, s)-Nets in Base 3

Best Known (166−66, 166, s)-Nets in Base 3

(166−66, 166, 148)-Net over F₃ — Constructive and digital

Digital (100, 166, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 83, 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]

(166−66, 166, 162)-Net over F₃ — Digital

Digital (100, 166, 162)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(166−66, 166, 1621)-Net in Base 3 — Upper bound on s

There is no (100, 166, 1622)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 181614 978826 443459 121224 687778 376091 998956 031245 264085 937199 245758 676328 256621 > 3¹⁶⁶ [i]