MinT - Best Known (155−45, 155, s)-Nets in Base 3

Best Known (155−45, 155, s)-Nets in Base 3

(155−45, 155, 228)-Net over F₃ — Constructive and digital

Digital (110, 155, 228)-net over F₃, using

1 times m-reduction [i] based on digital (110, 156, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 52, 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]

(155−45, 155, 398)-Net over F₃ — Digital

Digital (110, 155, 398)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−45, 155, 9879)-Net in Base 3 — Upper bound on s

There is no (110, 155, 9880)-net in base 3, because

1 times m-reduction [i] would yield (110, 154, 9880)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 30 012094 770338 494832 054896 954687 248118 391231 124506 158731 899190 857663 392401 > 3¹⁵⁴ [i]