MinT - Best Known (151, 151+46, s)-Nets in Base 3

Best Known (151, 151+46, s)-Nets in Base 3

(151, 151+46, 464)-Net over F₃ — Constructive and digital

Digital (151, 197, 464)-net over F₃, using

3¹ times duplication [i] based on digital (150, 196, 464)-net over F₃, using
- t-expansion [i] based on digital (149, 196, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 49, 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]

(151, 151+46, 1103)-Net over F₃ — Digital

Digital (151, 197, 1103)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(151, 151+46, 57531)-Net in Base 3 — Upper bound on s

There is no (151, 197, 57532)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9840 527900 182185 333153 113689 670140 535328 938306 276784 646546 858703 027665 888599 264381 617091 159057 > 3¹⁹⁷ [i]