MinT - Best Known (46, 46+39, s)-Nets in Base 3

Best Known (46, 46+39, s)-Nets in Base 3

(46, 46+39, 56)-Net over F₃ — Constructive and digital

Digital (46, 85, 56)-net over F₃, using

1 times m-reduction [i] based on digital (46, 86, 56)-net over F₃, using
- trace code for nets [i] based on digital (3, 43, 28)-net over F₉, using
  - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]

(46, 46+39, 63)-Net over F₃ — Digital

Digital (46, 85, 63)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 46+39, 491)-Net in Base 3 — Upper bound on s

There is no (46, 85, 492)-net in base 3, because

1 times m-reduction [i] would yield (46, 84, 492)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 12076 538741 998808 749773 030146 509497 633105 > 3⁸⁴ [i]