MinT - Best Known (186, 186+57, s)-Nets in Base 3

Best Known (186, 186+57, s)-Nets in Base 3

(186, 186+57, 464)-Net over F₃ — Constructive and digital

Digital (186, 243, 464)-net over F₃, using

t-expansion [i] based on digital (185, 243, 464)-net over F₃, using
- 1 times m-reduction [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+57, 1292)-Net over F₃ — Digital

Digital (186, 243, 1292)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 186+57, 75076)-Net in Base 3 — Upper bound on s

There is no (186, 243, 75077)-net in base 3, because

1 times m-reduction [i] would yield (186, 242, 75077)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29 063320 582837 958355 458138 289029 077791 620669 506011 235262 816790 133322 242173 315015 018966 853601 304914 689456 927929 319409 > 3²⁴² [i]