MinT - Best Known (127, 127+87, s)-Nets in Base 3

Best Known (127, 127+87, s)-Nets in Base 3

(127, 127+87, 148)-Net over F₃ — Constructive and digital

Digital (127, 214, 148)-net over F₃, using

6 times m-reduction [i] based on digital (127, 220, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 110, 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]

(127, 127+87, 189)-Net over F₃ — Digital

Digital (127, 214, 189)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+87, 1907)-Net in Base 3 — Upper bound on s

There is no (127, 214, 1908)-net in base 3, because

1 times m-reduction [i] would yield (127, 213, 1908)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 432276 269493 217648 933553 574953 888016 085490 374429 587367 798207 498483 715214 667755 212491 550629 557662 983345 > 3²¹³ [i]