MinT - Best Known (66, 66+56, s)-Nets in Base 3

Best Known (66, 66+56, s)-Nets in Base 3

(66, 66+56, 64)-Net over F₃ — Constructive and digital

Digital (66, 122, 64)-net over F₃, using

trace code for nets [i] based on digital (5, 61, 32)-net over F₉, using
- net from sequence [i] based on digital (5, 31)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 5 and N(F) ≥ 32, using
    - a function field by GarcÃa and Quoos [i]

(66, 66+56, 84)-Net over F₃ — Digital

Digital (66, 122, 84)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+56, 650)-Net in Base 3 — Upper bound on s

There is no (66, 122, 651)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16592 837498 851435 358693 211277 603055 185096 451558 262556 173225 > 3¹²² [i]