MinT - Best Known (128, 128+86, s)-Nets in Base 3

Best Known (128, 128+86, s)-Nets in Base 3

(128, 128+86, 148)-Net over F₃ — Constructive and digital

Digital (128, 214, 148)-net over F₃, using

8 times m-reduction [i] based on digital (128, 222, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 111, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(128, 128+86, 195)-Net over F₃ — Digital

Digital (128, 214, 195)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(128, 128+86, 1957)-Net in Base 3 — Upper bound on s

There is no (128, 214, 1958)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 284170 791671 381484 033422 653811 521211 876989 035863 517078 049662 281939 800193 739547 884736 680658 205143 025489 > 3²¹⁴ [i]