MinT - Best Known (100, 140, s)-Nets in Base 3

Best Known (100, 140, s)-Nets in Base 3

(100, 140, 228)-Net over F₃ — Constructive and digital

Digital (100, 140, 228)-net over F₃, using

1 times m-reduction [i] based on digital (100, 141, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 47, 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]

(100, 140, 388)-Net over F₃ — Digital

Digital (100, 140, 388)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(100, 140, 9061)-Net in Base 3 — Upper bound on s

There is no (100, 140, 9062)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 6 274950 484065 579904 390575 642415 023132 691789 019108 901538 528484 219049 > 3¹⁴⁰ [i]