MinT - Best Known (241−57, 241, s)-Nets in Base 3

Best Known (241−57, 241, s)-Nets in Base 3

(241−57, 241, 464)-Net over F₃ — Constructive and digital

Digital (184, 241, 464)-net over F₃, using

3¹ times duplication [i] based on digital (183, 240, 464)-net over F₃, using
- t-expansion [i] based on digital (182, 240, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 60, 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]

(241−57, 241, 1240)-Net over F₃ — Digital

Digital (184, 241, 1240)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−57, 241, 69408)-Net in Base 3 — Upper bound on s

There is no (184, 241, 69409)-net in base 3, because

1 times m-reduction [i] would yield (184, 240, 69409)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 229663 451381 622116 708496 615213 438016 809158 418800 913254 320296 063964 797371 557780 181615 196152 126222 944833 080348 312625 > 3²⁴⁰ [i]