MinT - Best Known (118−48, 118, s)-Nets in Base 3

Best Known (118−48, 118, s)-Nets in Base 3

(118−48, 118, 80)-Net over F₃ — Constructive and digital

Digital (70, 118, 80)-net over F₃, using

6 times m-reduction [i] based on digital (70, 124, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 62, 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]

(118−48, 118, 115)-Net over F₃ — Digital

Digital (70, 118, 115)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(118−48, 118, 1063)-Net in Base 3 — Upper bound on s

There is no (70, 118, 1064)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 201 513726 440607 486180 230556 159651 822173 871060 678364 011777 > 3¹¹⁸ [i]