MinT - Best Known (119, 119+68, s)-Nets in Base 3

Best Known (119, 119+68, s)-Nets in Base 3

(119, 119+68, 156)-Net over F₃ — Constructive and digital

Digital (119, 187, 156)-net over F₃, using

7 times m-reduction [i] based on digital (119, 194, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 97, 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]

(119, 119+68, 231)-Net over F₃ — Digital

Digital (119, 187, 231)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(119, 119+68, 2815)-Net in Base 3 — Upper bound on s

There is no (119, 187, 2816)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 168322 684983 690025 860300 603583 393219 227423 634816 610372 081973 974007 407295 581547 018162 176513 > 3¹⁸⁷ [i]