MinT - Best Known (158−47, 158, s)-Nets in Base 3

Best Known (158−47, 158, s)-Nets in Base 3

(158−47, 158, 204)-Net over F₃ — Constructive and digital

Digital (111, 158, 204)-net over F₃, using

1 times m-reduction [i] based on digital (111, 159, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 53, 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]

(158−47, 158, 373)-Net over F₃ — Digital

Digital (111, 158, 373)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−47, 158, 8494)-Net in Base 3 — Upper bound on s

There is no (111, 158, 8495)-net in base 3, because

1 times m-reduction [i] would yield (111, 157, 8495)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 809 740070 535277 560700 733365 333158 366566 751774 322809 101010 049207 637810 993043 > 3¹⁵⁷ [i]