MinT - Best Known (140−37, 140, s)-Nets in Base 3

Best Known (140−37, 140, s)-Nets in Base 3

(140−37, 140, 264)-Net over F₃ — Constructive and digital

Digital (103, 140, 264)-net over F₃, using

1 times m-reduction [i] based on digital (103, 141, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 47, 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]

(140−37, 140, 517)-Net over F₃ — Digital

Digital (103, 140, 517)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−37, 140, 18244)-Net in Base 3 — Upper bound on s

There is no (103, 140, 18245)-net in base 3, because

1 times m-reduction [i] would yield (103, 139, 18245)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2 090643 676426 491675 438923 474462 930101 045639 596022 297434 784706 893585 > 3¹³⁹ [i]