MinT - Best Known (199−89, 199, s)-Nets in Base 3

Best Known (199−89, 199, s)-Nets in Base 3

(199−89, 199, 80)-Net over F₃ — Constructive and digital

Digital (110, 199, 80)-net over F₃, using

5 times m-reduction [i] based on digital (110, 204, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 102, 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]

(199−89, 199, 136)-Net over F₃ — Digital

Digital (110, 199, 136)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(199−89, 199, 1167)-Net in Base 3 — Upper bound on s

There is no (110, 199, 1168)-net in base 3, because

1 times m-reduction [i] would yield (110, 198, 1168)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29982 115291 558003 080463 221336 725042 117853 858304 556437 629685 270839 101382 444704 031066 212834 347905 > 3¹⁹⁸ [i]