MinT - Best Known (243−98, 243, s)-Nets in Base 3

Best Known (243−98, 243, s)-Nets in Base 3

(243−98, 243, 156)-Net over F₃ — Constructive and digital

Digital (145, 243, 156)-net over F₃, using

3 times m-reduction [i] based on digital (145, 246, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 123, 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]

(243−98, 243, 217)-Net over F₃ — Digital

Digital (145, 243, 217)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−98, 243, 2172)-Net in Base 3 — Upper bound on s

There is no (145, 243, 2173)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 88 685229 383150 583474 951326 652077 947014 155946 767915 970161 775261 523904 767505 904904 791758 792641 619217 164778 966476 797755 > 3²⁴³ [i]