MinT - Best Known (120, 120+44, s)-Nets in Base 3

Best Known (120, 120+44, s)-Nets in Base 3

(120, 120+44, 282)-Net over F₃ — Constructive and digital

Digital (120, 164, 282)-net over F₃, using

1 times m-reduction [i] based on digital (120, 165, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 55, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(120, 120+44, 552)-Net over F₃ — Digital

Digital (120, 164, 552)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+44, 16291)-Net in Base 3 — Upper bound on s

There is no (120, 164, 16292)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 769797 653737 561469 694563 521489 563373 168332 029092 168968 179368 814471 716463 517593 > 3¹⁶⁴ [i]