MinT - Best Known (118, 118+64, s)-Nets in Base 3

Best Known (118, 118+64, s)-Nets in Base 3

(118, 118+64, 156)-Net over F₃ — Constructive and digital

Digital (118, 182, 156)-net over F₃, using

10 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]

(118, 118+64, 250)-Net over F₃ — Digital

Digital (118, 182, 250)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(118, 118+64, 3275)-Net in Base 3 — Upper bound on s

There is no (118, 182, 3276)-net in base 3, because

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]