MinT - Best Known (104−66, 104, s)-Nets in Base 3

Best Known (104−66, 104, s)-Nets in Base 3

(104−66, 104, 38)-Net over F₃ — Constructive and digital

Digital (38, 104, 38)-net over F₃, using

t-expansion [i] based on digital (32, 104, 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]

(104−66, 104, 52)-Net over F₃ — Digital

Digital (38, 104, 52)-net over F₃, using

t-expansion [i] based on digital (37, 104, 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]

(104−66, 104, 129)-Net in Base 3 — Upper bound on s

There is no (38, 104, 130)-net in base 3, because

1 times m-reduction [i] would yield (38, 103, 130)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹⁰³, 130, S₃, 65), but
  - the linear programming bound shows that MÂ â‰¥ 245 717769 990125 080884 183592 612860 937940 609304 274570 786762 609437 / 17 549689 290749 > 3¹⁰³ [i]