MinT - Best Known (120, 120+88, s)-Nets in Base 3

Best Known (120, 120+88, s)-Nets in Base 3

(120, 120+88, 128)-Net over F₃ — Constructive and digital

Digital (120, 208, 128)-net over F₃, using

6 times m-reduction [i] based on digital (120, 214, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 107, 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]

(120, 120+88, 165)-Net over F₃ — Digital

Digital (120, 208, 165)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+88, 1510)-Net in Base 3 — Upper bound on s

There is no (120, 208, 1511)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1756 142214 391751 394451 207222 322352 243816 874170 979582 610152 802487 482396 540667 185523 608754 158764 266153 > 3²⁰⁸ [i]