MinT - Best Known (182−79, 182, s)-Nets in Base 3

Best Known (182−79, 182, s)-Nets in Base 3

(182−79, 182, 80)-Net over F₃ — Constructive and digital

Digital (103, 182, 80)-net over F₃, using

8 times m-reduction [i] based on digital (103, 190, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 95, 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]

(182−79, 182, 137)-Net over F₃ — Digital

Digital (103, 182, 137)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(182−79, 182, 1223)-Net in Base 3 — Upper bound on s

There is no (103, 182, 1224)-net in base 3, because

1 times m-reduction [i] would yield (103, 181, 1224)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 235 580091 576523 672730 077918 712348 180061 437112 256398 151822 980039 119957 016259 874875 412577 > 3¹⁸¹ [i]