MinT - Best Known (140, 140+60, s)-Nets in Base 3

Best Known (140, 140+60, s)-Nets in Base 3

(140, 140+60, 228)-Net over F₃ — Constructive and digital

Digital (140, 200, 228)-net over F₃, using

1 times m-reduction [i] based on digital (140, 201, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 67, 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]

(140, 140+60, 443)-Net over F₃ — Digital

Digital (140, 200, 443)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140, 140+60, 9102)-Net in Base 3 — Upper bound on s

There is no (140, 200, 9103)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 265995 021261 583397 375004 092777 144625 237152 064666 049761 312949 105158 336556 937063 648807 968203 771493 > 3²⁰⁰ [i]