MinT - Best Known (126, 126+47, s)-Nets in Base 3

Best Known (126, 126+47, s)-Nets in Base 3

(126, 126+47, 282)-Net over F₃ — Constructive and digital

Digital (126, 173, 282)-net over F₃, using

1 times m-reduction [i] based on digital (126, 174, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 58, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(126, 126+47, 550)-Net over F₃ — Digital

Digital (126, 173, 550)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(126, 126+47, 17414)-Net in Base 3 — Upper bound on s

There is no (126, 173, 17415)-net in base 3, because

1 times m-reduction [i] would yield (126, 172, 17415)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 11623 196899 157899 744265 696520 375484 971865 500164 863295 273284 153959 177692 767488 816499 > 3¹⁷² [i]