MinT - Best Known (185−83, 185, s)-Nets in Base 3

Best Known (185−83, 185, s)-Nets in Base 3

(185−83, 185, 80)-Net over F₃ — Constructive and digital

Digital (102, 185, 80)-net over F₃, using

3 times m-reduction [i] based on digital (102, 188, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 94, 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]

(185−83, 185, 127)-Net over F₃ — Digital

Digital (102, 185, 127)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−83, 185, 1077)-Net in Base 3 — Upper bound on s

There is no (102, 185, 1078)-net in base 3, because

1 times m-reduction [i] would yield (102, 184, 1078)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6343 306982 896471 288892 742404 609473 781195 819005 858373 465567 289844 789343 463870 925629 933981 > 3¹⁸⁴ [i]