MinT - Best Known (125−37, 125, s)-Nets in Base 3

Best Known (125−37, 125, s)-Nets in Base 3

(125−37, 125, 192)-Net over F₃ — Constructive and digital

Digital (88, 125, 192)-net over F₃, using

1 times m-reduction [i] based on digital (88, 126, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 42, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(125−37, 125, 314)-Net over F₃ — Digital

Digital (88, 125, 314)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(125−37, 125, 7292)-Net in Base 3 — Upper bound on s

There is no (88, 125, 7293)-net in base 3, because

1 times m-reduction [i] would yield (88, 124, 7293)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 145622 217048 819189 629125 188312 336681 495863 619083 708194 746945 > 3¹²⁴ [i]