MinT - Best Known (66, 66+54, s)-Nets in Base 3

Best Known (66, 66+54, s)-Nets in Base 3

(66, 66+54, 68)-Net over F₃ — Constructive and digital

Digital (66, 120, 68)-net over F₃, using

trace code for nets [i] based on digital (6, 60, 34)-net over F₉, using
- net from sequence [i] based on digital (6, 33)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 6 and N(F) ≥ 34, using
    - a function field by SÃ©mirat [i]

(66, 66+54, 88)-Net over F₃ — Digital

Digital (66, 120, 88)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(66, 66+54, 694)-Net in Base 3 — Upper bound on s

There is no (66, 120, 695)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1806 017880 995186 716744 011608 550650 177885 973326 375042 059307 > 3¹²⁰ [i]