MinT - Best Known (37, 102, s)-Nets in Base 3

Best Known (37, 102, s)-Nets in Base 3

(37, 102, 38)-Net over F₃ — Constructive and digital

Digital (37, 102, 38)-net over F₃, using

t-expansion [i] based on digital (32, 102, 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, 102, 52)-Net over F₃ — Digital

Digital (37, 102, 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, 102, 124)-Net in Base 3 — Upper bound on s

There is no (37, 102, 125)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰², 125, S₃, 65), but
- the linear programming bound shows that MÂ â‰¥ 82769 748454 520344 172235 733433 653475 678772 427150 151046 492171 / 16360 421572 > 3¹⁰² [i]