MinT - Best Known (183−65, 183, s)-Nets in Base 3

Best Known (183−65, 183, s)-Nets in Base 3

(183−65, 183, 156)-Net over F₃ — Constructive and digital

Digital (118, 183, 156)-net over F₃, using

9 times m-reduction [i] based on digital (118, 192, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 96, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(183−65, 183, 243)-Net over F₃ — Digital

Digital (118, 183, 243)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(183−65, 183, 3275)-Net in Base 3 — Upper bound on s

There is no (118, 183, 3276)-net in base 3, because

1 times m-reduction [i] would yield (118, 182, 3276)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 685 897903 047811 934709 654238 787774 143728 035859 438215 945740 216122 317812 307954 657747 478785 > 3¹⁸² [i]