MinT - Best Known (127, 218, s)-Nets in Base 3

Best Known (127, 218, s)-Nets in Base 3

(127, 218, 148)-Net over F₃ — Constructive and digital

Digital (127, 218, 148)-net over F₃, using

2 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, 218, 179)-Net over F₃ — Digital

Digital (127, 218, 179)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(127, 218, 1717)-Net in Base 3 — Upper bound on s

There is no (127, 218, 1718)-net in base 3, because

1 times m-reduction [i] would yield (127, 217, 1718)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 611378 330233 132697 555784 787321 075306 978997 002092 665981 368277 056137 131001 831148 268102 530542 136916 299637 > 3²¹⁷ [i]