MinT - Best Known (186, 242, s)-Nets in Base 3

Best Known (186, 242, s)-Nets in Base 3

(186, 242, 600)-Net over F₃ — Constructive and digital

Digital (186, 242, 600)-net over F₃, using

3² times duplication [i] based on digital (184, 240, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 60, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(186, 242, 1364)-Net over F₃ — Digital

Digital (186, 242, 1364)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(186, 242, 75076)-Net in Base 3 — Upper bound on s

There is no (186, 242, 75077)-net in base 3, because

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]