MinT - Best Known (37, 37+59, s)-Nets in Base 3

Best Known (37, 37+59, s)-Nets in Base 3

(37, 37+59, 38)-Net over F₃ — Constructive and digital

Digital (37, 96, 38)-net over F₃, using

t-expansion [i] based on digital (32, 96, 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]

(37, 37+59, 52)-Net over F₃ — Digital

Digital (37, 96, 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]

(37, 37+59, 143)-Net in Base 3 — Upper bound on s

There is no (37, 96, 144)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹⁶, 144, S₃, 59), but
- the linear programming bound shows that MÂ â‰¥ 2236 401438 247250 718182 900374 183456 399210 453427 110900 255699 874712 354347 141530 819695 / 326304 173287 366006 276464 537104 634223 > 3⁹⁶ [i]