MinT - Best Known (82, 82+58, s)-Nets in Base 3

Best Known (82, 82+58, s)-Nets in Base 3

(82, 82+58, 80)-Net over F₃ — Constructive and digital

Digital (82, 140, 80)-net over F₃, using

8 times m-reduction [i] based on digital (82, 148, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 74, 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]

(82, 82+58, 125)-Net over F₃ — Digital

Digital (82, 140, 125)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+58, 1145)-Net in Base 3 — Upper bound on s

There is no (82, 140, 1146)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 397488 611743 978023 618087 946933 964083 311803 710238 229585 787749 358173 > 3¹⁴⁰ [i]