MinT - Best Known (198−84, 198, s)-Nets in Base 3

Best Known (198−84, 198, s)-Nets in Base 3

(198−84, 198, 128)-Net over F₃ — Constructive and digital

Digital (114, 198, 128)-net over F₃, using

4 times m-reduction [i] based on digital (114, 202, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 101, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(198−84, 198, 157)-Net over F₃ — Digital

Digital (114, 198, 157)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(198−84, 198, 1424)-Net in Base 3 — Upper bound on s

There is no (114, 198, 1425)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29745 582023 789819 650743 238217 752995 427763 038333 913714 840014 947794 709264 641733 126067 673386 754505 > 3¹⁹⁸ [i]