MinT - Best Known (84−47, 84, s)-Nets in Base 3

Best Known (84−47, 84, s)-Nets in Base 3

(84−47, 84, 38)-Net over F₃ — Constructive and digital

Digital (37, 84, 38)-net over F₃, using

t-expansion [i] based on digital (32, 84, 38)-net over F₃, using
- net from sequence [i] based on digital (32, 37)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 32 and N(F) ≥ 38, using
    - an explicitly constructive algebraic function field [i]

(84−47, 84, 52)-Net over F₃ — Digital

Digital (37, 84, 52)-net over F₃, using

net from sequence [i] based on digital (37, 51)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 37 and N(F) ≥ 52, using
  - a curve from the manYPoints database [i]

(84−47, 84, 226)-Net in Base 3 — Upper bound on s

There is no (37, 84, 227)-net in base 3, because

1 times m-reduction [i] would yield (37, 83, 227)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4085 658108 343385 290709 385979 280094 669411 > 3⁸³ [i]