MinT - Best Known (163−48, 163, s)-Nets in Base 3

Best Known (163−48, 163, s)-Nets in Base 3

(163−48, 163, 228)-Net over F₃ — Constructive and digital

Digital (115, 163, 228)-net over F₃, using

3¹ times duplication [i] based on digital (114, 162, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 54, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(163−48, 163, 396)-Net over F₃ — Digital

Digital (115, 163, 396)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−48, 163, 8503)-Net in Base 3 — Upper bound on s

There is no (115, 163, 8504)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 591156 740699 496852 998791 594385 316482 241103 238986 553626 024416 596675 554072 657153 > 3¹⁶³ [i]