MinT - Best Known (38, 38+57, s)-Nets in Base 3

Best Known (38, 38+57, s)-Nets in Base 3

(38, 38+57, 38)-Net over F₃ — Constructive and digital

Digital (38, 95, 38)-net over F₃, using

t-expansion [i] based on digital (32, 95, 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]

(38, 38+57, 52)-Net over F₃ — Digital

Digital (38, 95, 52)-net over F₃, using

t-expansion [i] based on digital (37, 95, 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]

(38, 38+57, 199)-Net in Base 3 — Upper bound on s

There is no (38, 95, 200)-net in base 3, because

1 times m-reduction [i] would yield (38, 94, 200)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 741 098692 074236 408220 707575 760619 787186 318657 > 3⁹⁴ [i]