MinT - Best Known (157−43, 157, s)-Nets in Base 3

Best Known (157−43, 157, s)-Nets in Base 3

(157−43, 157, 264)-Net over F₃ — Constructive and digital

Digital (114, 157, 264)-net over F₃, using

3¹ times duplication [i] based on digital (113, 156, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 52, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(157−43, 157, 494)-Net over F₃ — Digital

Digital (114, 157, 494)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(157−43, 157, 15177)-Net in Base 3 — Upper bound on s

There is no (114, 157, 15178)-net in base 3, because

1 times m-reduction [i] would yield (114, 156, 15178)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 269 832554 261962 052339 230315 369180 224538 932336 038916 692035 934281 357666 370637 > 3¹⁵⁶ [i]