MinT - Best Known (123, 123+36, s)-Nets in Base 3

Best Known (123, 123+36, s)-Nets in Base 3

(123, 123+36, 464)-Net over F₃ — Constructive and digital

Digital (123, 159, 464)-net over F₃, using

t-expansion [i] based on digital (122, 159, 464)-net over F₃, using
- 1 times m-reduction [i] based on digital (122, 160, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 40, 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]

(123, 123+36, 1040)-Net over F₃ — Digital

Digital (123, 159, 1040)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(123, 123+36, 61879)-Net in Base 3 — Upper bound on s

There is no (123, 159, 61880)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7283 071828 486707 566112 180135 114339 881964 003891 684495 836122 430156 027591 161297 > 3¹⁵⁹ [i]