MinT - Best Known (163−49, 163, s)-Nets in Base 3

Best Known (163−49, 163, s)-Nets in Base 3

(163−49, 163, 204)-Net over F₃ — Constructive and digital

Digital (114, 163, 204)-net over F₃, using

3¹ times duplication [i] based on digital (113, 162, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 54, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(163−49, 163, 370)-Net over F₃ — Digital

Digital (114, 163, 370)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(163−49, 163, 8121)-Net in Base 3 — Upper bound on s

There is no (114, 163, 8122)-net in base 3, because

1 times m-reduction [i] would yield (114, 162, 8122)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 196790 420688 716343 066041 958595 597191 602652 683086 093862 827924 968743 002343 812977 > 3¹⁶² [i]