MinT - Best Known (194−74, 194, s)-Nets in Base 3

Best Known (194−74, 194, s)-Nets in Base 3

(194−74, 194, 156)-Net over F₃ — Constructive and digital

Digital (120, 194, 156)-net over F₃, using

2 times m-reduction [i] based on digital (120, 196, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 98, 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]

(194−74, 194, 209)-Net over F₃ — Digital

Digital (120, 194, 209)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(194−74, 194, 2289)-Net in Base 3 — Upper bound on s

There is no (120, 194, 2290)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 367 915712 825991 425487 663380 115350 650134 258084 392454 000092 589376 258296 392179 720903 369679 009085 > 3¹⁹⁴ [i]