MinT - Best Known (33, 33+58, s)-Nets in Base 3

Best Known (33, 33+58, s)-Nets in Base 3

(33, 33+58, 38)-Net over F₃ — Constructive and digital

Digital (33, 91, 38)-net over F₃, using

t-expansion [i] based on digital (32, 91, 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+58, 46)-Net over F₃ — Digital

Digital (33, 91, 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+58, 113)-Net in Base 3 — Upper bound on s

There is no (33, 91, 114)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹¹, 114, S₃, 58), but
- the linear programming bound shows that MÂ â‰¥ 11863 026293 532170 260695 793154 092472 693091 642420 543205 235073 / 439 628052 325961 > 3⁹¹ [i]