MinT - Best Known (62−19, 62, s)-Nets in Base 3

Best Known (62−19, 62, s)-Nets in Base 3

(62−19, 62, 114)-Net over F₃ — Constructive and digital

Digital (43, 62, 114)-net over F₃, using

1 times m-reduction [i] based on digital (43, 63, 114)-net over F₃, using
- trace code for nets [i] based on digital (1, 21, 38)-net over F₂₇, using
  - net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(62−19, 62, 172)-Net over F₃ — Digital

Digital (43, 62, 172)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(62−19, 62, 3544)-Net in Base 3 — Upper bound on s

There is no (43, 62, 3545)-net in base 3, because

1 times m-reduction [i] would yield (43, 61, 3545)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 127468 955662 370344 846643 444499 > 3⁶¹ [i]