MinT - Best Known (182−81, 182, s)-Nets in Base 3

Best Known (182−81, 182, s)-Nets in Base 3

(182−81, 182, 80)-Net over F₃ — Constructive and digital

Digital (101, 182, 80)-net over F₃, using

4 times m-reduction [i] based on digital (101, 186, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 93, 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]

(182−81, 182, 128)-Net over F₃ — Digital

Digital (101, 182, 128)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−81, 182, 1097)-Net in Base 3 — Upper bound on s

There is no (101, 182, 1098)-net in base 3, because

1 times m-reduction [i] would yield (101, 181, 1098)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228 573165 841924 070761 997439 881260 387455 386250 300708 797686 037035 211572 520026 305504 607249 > 3¹⁸¹ [i]