MinT - Best Known (96−61, 96, s)-Nets in Base 3

Best Known (96−61, 96, s)-Nets in Base 3

(96−61, 96, 38)-Net over F₃ — Constructive and digital

Digital (35, 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]

(96−61, 96, 47)-Net over F₃ — Digital

Digital (35, 96, 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]

(96−61, 96, 121)-Net in Base 3 — Upper bound on s

There is no (35, 96, 122)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁹⁶, 122, S₃, 61), but
- the linear programming bound shows that MÂ â‰¥ 1640 916143 405505 709852 047392 464204 188997 334202 214159 700584 446051 / 199460 399430 245723 > 3⁹⁶ [i]