MinT - Best Known (209−49, 209, s)-Nets in Base 3

Best Known (209−49, 209, s)-Nets in Base 3

(209−49, 209, 464)-Net over F₃ — Constructive and digital

Digital (160, 209, 464)-net over F₃, using

3¹ times duplication [i] based on digital (159, 208, 464)-net over F₃, using
- t-expansion [i] based on digital (158, 208, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 52, 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]

(209−49, 209, 1144)-Net over F₃ — Digital

Digital (160, 209, 1144)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(209−49, 209, 66869)-Net in Base 3 — Upper bound on s

There is no (160, 209, 66870)-net in base 3, because

1 times m-reduction [i] would yield (160, 208, 66870)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1742 720582 597425 073570 252428 150650 129549 178998 778283 653243 448482 526897 397826 784679 253687 815194 302833 > 3²⁰⁸ [i]