MinT - Best Known (217−89, 217, s)-Nets in Base 3

Best Known (217−89, 217, s)-Nets in Base 3

(217−89, 217, 148)-Net over F₃ — Constructive and digital

Digital (128, 217, 148)-net over F₃, using

5 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]

(217−89, 217, 187)-Net over F₃ — Digital

Digital (128, 217, 187)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−89, 217, 1854)-Net in Base 3 — Upper bound on s

There is no (128, 217, 1855)-net in base 3, because

1 times m-reduction [i] would yield (128, 216, 1855)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11 658719 014107 321104 658249 292322 544549 963747 834412 297137 924960 930180 217148 009010 488563 028731 151584 564137 > 3²¹⁶ [i]