MinT - Best Known (142, 142+57, s)-Nets in Base 3

Best Known (142, 142+57, s)-Nets in Base 3

(142, 142+57, 264)-Net over F₃ — Constructive and digital

Digital (142, 199, 264)-net over F₃, using

3¹ times duplication [i] based on digital (141, 198, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 66, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(142, 142+57, 514)-Net over F₃ — Digital

Digital (142, 199, 514)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(142, 142+57, 13335)-Net in Base 3 — Upper bound on s

There is no (142, 199, 13336)-net in base 3, because

1 times m-reduction [i] would yield (142, 198, 13336)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29542 256127 186862 513511 088287 551161 866555 095582 809430 088614 876951 966379 489610 958765 120894 284993 > 3¹⁹⁸ [i]