MinT - Best Known (33, 33+62, s)-Nets in Base 3

Best Known (33, 33+62, s)-Nets in Base 3

(33, 33+62, 38)-Net over F₃ — Constructive and digital

Digital (33, 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]

(33, 33+62, 46)-Net over F₃ — Digital

Digital (33, 95, 46)-net over F₃, using

net from sequence [i] based on digital (33, 45)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 33 and N(F) ≥ 46, using
  - a curve from the manYPoints database [i]

(33, 33+62, 109)-Net in Base 3 — Upper bound on s

There is no (33, 95, 110)-net in base 3, because

1 times m-reduction [i] would yield (33, 94, 110)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3⁹⁴, 110, S₃, 61), but
  - the linear programming bound shows that MÂ â‰¥ 9142 281840 265149 001255 783980 912355 756462 685332 775739 / 12 834031 > 3⁹⁴ [i]