MinT - Best Known (141, 141+41, s)-Nets in Base 3

Best Known (141, 141+41, s)-Nets in Base 3

(141, 141+41, 600)-Net over F₃ — Constructive and digital

Digital (141, 182, 600)-net over F₃, using

3² times duplication [i] based on digital (139, 180, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 45, 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]

(141, 141+41, 1188)-Net over F₃ — Digital

Digital (141, 182, 1188)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+41, 86322)-Net in Base 3 — Upper bound on s

There is no (141, 182, 86323)-net in base 3, because

1 times m-reduction [i] would yield (141, 181, 86323)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 542774 961634 414409 291659 871963 651258 754473 019277 965628 732811 318442 537831 374206 979001 > 3¹⁸¹ [i]