MinT - Best Known (183, 243, s)-Nets in Base 3

Best Known (183, 243, s)-Nets in Base 3

(183, 243, 328)-Net over F₃ — Constructive and digital

Digital (183, 243, 328)-net over F₃, using

1 times m-reduction [i] based on digital (183, 244, 328)-net over F₃, using
- trace code for nets [i] based on digital (0, 61, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]

(183, 243, 1049)-Net over F₃ — Digital

Digital (183, 243, 1049)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(183, 243, 44070)-Net in Base 3 — Upper bound on s

There is no (183, 243, 44071)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 205276 170812 597976 496232 414183 570787 273796 290232 869378 283128 767985 772635 304394 842999 094494 690968 887397 225225 959637 > 3²⁴³ [i]