MinT - Best Known (190−46, 190, s)-Nets in Base 3

Best Known (190−46, 190, s)-Nets in Base 3

(190−46, 190, 400)-Net over F₃ — Constructive and digital

Digital (144, 190, 400)-net over F₃, using

3² times duplication [i] based on digital (142, 188, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 47, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(190−46, 190, 928)-Net over F₃ — Digital

Digital (144, 190, 928)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−46, 190, 41174)-Net in Base 3 — Upper bound on s

There is no (144, 190, 41175)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 500119 654688 925241 842222 257687 416390 849328 992668 678644 407497 146465 485561 079537 566199 249331 > 3¹⁹⁰ [i]