MinT - Best Known (120, 120+36, s)-Nets in Base 3

Best Known (120, 120+36, s)-Nets in Base 3

(120, 120+36, 464)-Net over F₃ — Constructive and digital

Digital (120, 156, 464)-net over F₃, using

t-expansion [i] based on digital (119, 156, 464)-net over F₃, using
- trace code for nets [i] based on digital (2, 39, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

(120, 120+36, 948)-Net over F₃ — Digital

Digital (120, 156, 948)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(120, 120+36, 51523)-Net in Base 3 — Upper bound on s

There is no (120, 156, 51524)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 269 789776 717006 157463 547227 955209 021677 603789 905195 963501 666429 533635 150265 > 3¹⁵⁶ [i]