MinT - Best Known (250−58, 250, s)-Nets in Base 3

Best Known (250−58, 250, s)-Nets in Base 3

(250−58, 250, 600)-Net over F₃ — Constructive and digital

Digital (192, 250, 600)-net over F₃, using

3² times duplication [i] based on digital (190, 248, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 62, 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]

(250−58, 250, 1386)-Net over F₃ — Digital

Digital (192, 250, 1386)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−58, 250, 75690)-Net in Base 3 — Upper bound on s

There is no (192, 250, 75691)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 190701 757896 275439 104081 338885 084451 536856 156010 279143 571498 337006 437402 704740 942882 742431 686405 907612 664826 564088 914207 > 3²⁵⁰ [i]