MinT - Best Known (190−83, 190, s)-Nets in Base 3

Best Known (190−83, 190, s)-Nets in Base 3

(190−83, 190, 80)-Net over F₃ — Constructive and digital

Digital (107, 190, 80)-net over F₃, using

8 times m-reduction [i] based on digital (107, 198, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 99, 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]

(190−83, 190, 140)-Net over F₃ — Digital

Digital (107, 190, 140)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(190−83, 190, 1237)-Net in Base 3 — Upper bound on s

There is no (107, 190, 1238)-net in base 3, because

1 times m-reduction [i] would yield (107, 189, 1238)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 531780 543258 281323 891772 343620 071458 236440 452415 938480 316378 521105 699420 610513 854605 462237 > 3¹⁸⁹ [i]