MinT - Best Known (173−76, 173, s)-Nets in Base 3

Best Known (173−76, 173, s)-Nets in Base 3

(173−76, 173, 80)-Net over F₃ — Constructive and digital

Digital (97, 173, 80)-net over F₃, using

5 times m-reduction [i] based on digital (97, 178, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 89, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(173−76, 173, 127)-Net over F₃ — Digital

Digital (97, 173, 127)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(173−76, 173, 1079)-Net in Base 3 — Upper bound on s

There is no (97, 173, 1080)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 35188 681055 838966 938817 906845 781353 686058 766062 472242 892942 296111 749891 957003 050321 > 3¹⁷³ [i]