MinT - Best Known (158−43, 158, s)-Nets in Base 3

Best Known (158−43, 158, s)-Nets in Base 3

(158−43, 158, 264)-Net over F₃ — Constructive and digital

Digital (115, 158, 264)-net over F₃, using

1 times m-reduction [i] based on digital (115, 159, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 53, 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]

(158−43, 158, 508)-Net over F₃ — Digital

Digital (115, 158, 508)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(158−43, 158, 15993)-Net in Base 3 — Upper bound on s

There is no (115, 158, 15994)-net in base 3, because

1 times m-reduction [i] would yield (115, 157, 15994)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 809 209194 345864 615680 430292 894644 803763 569433 284854 175006 499070 457146 766637 > 3¹⁵⁷ [i]