MinT - Best Known (115, 115+34, s)-Nets in Base 3

Best Known (115, 115+34, s)-Nets in Base 3

(115, 115+34, 464)-Net over F₃ — Constructive and digital

Digital (115, 149, 464)-net over F₃, using

3¹ times duplication [i] based on digital (114, 148, 464)-net over F₃, using
- t-expansion [i] based on digital (113, 148, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 37, 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]

(115, 115+34, 955)-Net over F₃ — Digital

Digital (115, 149, 955)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(115, 115+34, 54526)-Net in Base 3 — Upper bound on s

There is no (115, 149, 54527)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 123330 977777 591435 555259 073338 942048 606709 124977 353874 720731 002923 461087 > 3¹⁴⁹ [i]