MinT - Best Known (133−53, 133, s)-Nets in Base 3

Best Known (133−53, 133, s)-Nets in Base 3

(133−53, 133, 128)-Net over F₃ — Constructive and digital

Digital (80, 133, 128)-net over F₃, using

1 times m-reduction [i] based on digital (80, 134, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 67, 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]

(133−53, 133, 134)-Net over F₃ — Digital

Digital (80, 133, 134)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−53, 133, 1369)-Net in Base 3 — Upper bound on s

There is no (80, 133, 1370)-net in base 3, because

1 times m-reduction [i] would yield (80, 132, 1370)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 960 673748 683912 661184 157430 280379 849160 758126 314910 142739 750741 > 3¹³² [i]