MinT - Best Known (127, 127+92, s)-Nets in Base 3

Best Known (127, 127+92, s)-Nets in Base 3

(127, 127+92, 148)-Net over F₃ — Constructive and digital

Digital (127, 219, 148)-net over F₃, using

1 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+92, 176)-Net over F₃ — Digital

Digital (127, 219, 176)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 127+92, 1636)-Net in Base 3 — Upper bound on s

There is no (127, 219, 1637)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 312 416340 603251 846203 691475 414545 632034 254563 130075 034061 841731 954173 761186 142813 068675 997889 170549 803425 > 3²¹⁹ [i]