MinT - Best Known (167−73, 167, s)-Nets in Base 3

Best Known (167−73, 167, s)-Nets in Base 3

(167−73, 167, 80)-Net over F₃ — Constructive and digital

Digital (94, 167, 80)-net over F₃, using

5 times m-reduction [i] based on digital (94, 172, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 86, 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]

(167−73, 167, 125)-Net over F₃ — Digital

Digital (94, 167, 125)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(167−73, 167, 1096)-Net in Base 3 — Upper bound on s

There is no (94, 167, 1097)-net in base 3, because

1 times m-reduction [i] would yield (94, 166, 1097)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 16 055016 016180 858983 125874 091007 857251 582395 751861 355788 145358 466746 265206 983825 > 3¹⁶⁶ [i]