MinT - Best Known (40, 40+64, s)-Nets in Base 3

Best Known (40, 40+64, s)-Nets in Base 3

(40, 40+64, 42)-Net over F₃ — Constructive and digital

Digital (40, 104, 42)-net over F₃, using

t-expansion [i] based on digital (39, 104, 42)-net over F₃, using
- net from sequence [i] based on digital (39, 41)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 39 and N(F) ≥ 42, using
    - an explicitly constructive algebraic function field [i]

(40, 40+64, 56)-Net over F₃ — Digital

Digital (40, 104, 56)-net over F₃, using

net from sequence [i] based on digital (40, 55)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 40 and N(F) ≥ 56, using
  - a curve from the manYPoints database [i]

(40, 40+64, 149)-Net in Base 3 — Upper bound on s

There is no (40, 104, 150)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰⁴, 150, S₃, 64), but
- the linear programming bound shows that MÂ â‰¥ 24090 181438 283577 330749 823810 837311 447745 255812 944625 866896 355094 419670 238209 625117 / 575 377332 629089 480249 998798 828125 > 3¹⁰⁴ [i]