MinT - Best Known (84−49, 84, s)-Nets in Base 3

Best Known (84−49, 84, s)-Nets in Base 3

(84−49, 84, 38)-Net over F₃ — Constructive and digital

Digital (35, 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]

(84−49, 84, 47)-Net over F₃ — Digital

Digital (35, 84, 47)-net over F₃, using

net from sequence [i] based on digital (35, 46)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 35 and N(F) ≥ 47, using
  - a curve from the manYPoints database [i]

(84−49, 84, 196)-Net in Base 3 — Upper bound on s

There is no (35, 84, 197)-net in base 3, because

1 times m-reduction [i] would yield (35, 83, 197)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4233 356567 990429 220331 662183 232120 906017 > 3⁸³ [i]