MinT - Best Known (184−81, 184, s)-Nets in Base 3

Best Known (184−81, 184, s)-Nets in Base 3

(184−81, 184, 80)-Net over F₃ — Constructive and digital

Digital (103, 184, 80)-net over F₃, using

6 times m-reduction [i] based on digital (103, 190, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 95, 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]

(184−81, 184, 133)-Net over F₃ — Digital

Digital (103, 184, 133)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(184−81, 184, 1162)-Net in Base 3 — Upper bound on s

There is no (103, 184, 1163)-net in base 3, because

1 times m-reduction [i] would yield (103, 183, 1163)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2114 794546 507925 489544 127716 779539 121495 660948 644264 525795 631521 741776 785789 934724 069425 > 3¹⁸³ [i]