MinT - Best Known (176−42, 176, s)-Nets in Base 3

Best Known (176−42, 176, s)-Nets in Base 3

(176−42, 176, 464)-Net over F₃ — Constructive and digital

Digital (134, 176, 464)-net over F₃, using

trace code for nets [i] based on digital (2, 44, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(176−42, 176, 922)-Net over F₃ — Digital

Digital (134, 176, 922)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176−42, 176, 43250)-Net in Base 3 — Upper bound on s

There is no (134, 176, 43251)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 940862 362176 347669 592469 854916 113970 077058 658546 964276 582600 117066 734743 018643 747903 > 3¹⁷⁶ [i]