MinT - Best Known (217−88, 217, s)-Nets in Base 3

Best Known (217−88, 217, s)-Nets in Base 3

(217−88, 217, 148)-Net over F₃ — Constructive and digital

Digital (129, 217, 148)-net over F₃, using

7 times m-reduction [i] based on digital (129, 224, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 112, 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]

(217−88, 217, 193)-Net over F₃ — Digital

Digital (129, 217, 193)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(217−88, 217, 1902)-Net in Base 3 — Upper bound on s

There is no (129, 217, 1903)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 34 992793 528158 078897 135742 219220 546835 596167 035489 206746 366625 352862 829495 218837 372803 951747 580146 170025 > 3²¹⁷ [i]