MinT - Best Known (186, 186+58, s)-Nets in Base 3

Best Known (186, 186+58, s)-Nets in Base 3

(186, 186+58, 464)-Net over F₃ — Constructive and digital

Digital (186, 244, 464)-net over F₃, using

t-expansion [i] based on digital (185, 244, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 61, 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]

(186, 186+58, 1227)-Net over F₃ — Digital

Digital (186, 244, 1227)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 186+58, 60295)-Net in Base 3 — Upper bound on s

There is no (186, 244, 60296)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 261 606226 674312 824119 413578 584156 012657 588405 672567 838787 033093 643287 616434 977547 312306 731328 739715 734655 983525 485585 > 3²⁴⁴ [i]