MinT - Best Known (131, 131+57, s)-Nets in Base 3

Best Known (131, 131+57, s)-Nets in Base 3

(131, 131+57, 204)-Net over F₃ — Constructive and digital

Digital (131, 188, 204)-net over F₃, using

1 times m-reduction [i] based on digital (131, 189, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 63, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(131, 131+57, 406)-Net over F₃ — Digital

Digital (131, 188, 406)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+57, 8651)-Net in Base 3 — Upper bound on s

There is no (131, 188, 8652)-net in base 3, because

1 times m-reduction [i] would yield (131, 187, 8652)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 166916 753237 486487 608965 527302 901827 505994 544662 269241 028073 924562 051204 203120 186964 486465 > 3¹⁸⁷ [i]