MinT - Best Known (188−83, 188, s)-Nets in Base 3

Best Known (188−83, 188, s)-Nets in Base 3

(188−83, 188, 80)-Net over F₃ — Constructive and digital

Digital (105, 188, 80)-net over F₃, using

6 times m-reduction [i] based on digital (105, 194, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 97, 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]

(188−83, 188, 134)-Net over F₃ — Digital

Digital (105, 188, 134)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(188−83, 188, 1170)-Net in Base 3 — Upper bound on s

There is no (105, 188, 1171)-net in base 3, because

1 times m-reduction [i] would yield (105, 187, 1171)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 168228 799210 087355 527421 455944 307399 915125 841471 830871 510903 812782 330578 981325 753256 130455 > 3¹⁸⁷ [i]