MinT - Best Known (156, 156+55, s)-Nets in Base 3

Best Known (156, 156+55, s)-Nets in Base 3

(156, 156+55, 288)-Net over F₃ — Constructive and digital

Digital (156, 211, 288)-net over F₃, using

t-expansion [i] based on digital (155, 211, 288)-net over F₃, using
- 5 times m-reduction [i] based on digital (155, 216, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 72, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(156, 156+55, 756)-Net over F₃ — Digital

Digital (156, 211, 756)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(156, 156+55, 28048)-Net in Base 3 — Upper bound on s

There is no (156, 211, 28049)-net in base 3, because

1 times m-reduction [i] would yield (156, 210, 28049)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 15691 527086 378299 238210 372737 383882 355438 582837 604432 538420 950130 231719 492769 134328 453976 762919 239035 > 3²¹⁰ [i]