MinT - Best Known (180−66, 180, s)-Nets in Base 3

Best Known (180−66, 180, s)-Nets in Base 3

(180−66, 180, 156)-Net over F₃ — Constructive and digital

Digital (114, 180, 156)-net over F₃, using

4 times m-reduction [i] based on digital (114, 184, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 92, 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]

(180−66, 180, 219)-Net over F₃ — Digital

Digital (114, 180, 219)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180−66, 180, 2602)-Net in Base 3 — Upper bound on s

There is no (114, 180, 2603)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 76 362382 609211 373626 851404 622547 297405 511508 646863 596240 370973 983884 079277 215837 308183 > 3¹⁸⁰ [i]