MinT - Best Known (80, 80+46, s)-Nets in Base 3

Best Known (80, 80+46, s)-Nets in Base 3

(80, 80+46, 148)-Net over F₃ — Constructive and digital

Digital (80, 126, 148)-net over F₃, using

trace code for nets [i] based on digital (17, 63, 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]

(80, 80+46, 165)-Net over F₃ — Digital

Digital (80, 126, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 80+46, 1915)-Net in Base 3 — Upper bound on s

There is no (80, 126, 1916)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 325408 301347 223216 294439 043822 072200 135858 569310 942031 736081 > 3¹²⁶ [i]