MinT - Best Known (49, 49+43, s)-Nets in Base 3

Best Known (49, 49+43, s)-Nets in Base 3

(49, 49+43, 56)-Net over F₃ — Constructive and digital

Digital (49, 92, 56)-net over F₃, using

trace code for nets [i] based on digital (3, 46, 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]

(49, 49+43, 64)-Net over F₃ — Digital

Digital (49, 92, 64)-net over F₃, using

net from sequence [i] based on digital (49, 63)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 49 and N(F) ≥ 64, using
  - a curve from the manYPoints database [i]

(49, 49+43, 486)-Net in Base 3 — Upper bound on s

There is no (49, 92, 487)-net in base 3, because

1 times m-reduction [i] would yield (49, 91, 487)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 26 384249 337912 504173 674254 992289 854075 641575 > 3⁹¹ [i]