MinT - Best Known (193−71, 193, s)-Nets in Base 3

Best Known (193−71, 193, s)-Nets in Base 3

(193−71, 193, 156)-Net over F₃ — Constructive and digital

Digital (122, 193, 156)-net over F₃, using

7 times m-reduction [i] based on digital (122, 200, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 100, 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]

(193−71, 193, 230)-Net over F₃ — Digital

Digital (122, 193, 230)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−71, 193, 2846)-Net in Base 3 — Upper bound on s

There is no (122, 193, 2847)-net in base 3, because

1 times m-reduction [i] would yield (122, 192, 2847)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 510239 485382 349495 363977 569056 120740 658214 612084 798270 609888 883032 044919 348490 074897 958459 > 3¹⁹² [i]