MinT - Best Known (37, 100, s)-Nets in Base 3

Best Known (37, 100, s)-Nets in Base 3

(37, 100, 38)-Net over F₃ — Constructive and digital

Digital (37, 100, 38)-net over F₃, using

t-expansion [i] based on digital (32, 100, 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, 100, 52)-Net over F₃ — Digital

Digital (37, 100, 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, 100, 129)-Net in Base 3 — Upper bound on s

There is no (37, 100, 130)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3¹⁰⁰, 130, S₃, 63), but
- the linear programming bound shows that MÂ â‰¥ 3525 398943 718069 352990 234485 873786 665339 254979 039684 974246 436807 / 5155 452288 580352 > 3¹⁰⁰ [i]