MinT - Best Known (106−70, 106, s)-Nets in Base 3

Best Known (106−70, 106, s)-Nets in Base 3

(106−70, 106, 38)-Net over F₃ — Constructive and digital

Digital (36, 106, 38)-net over F₃, using

t-expansion [i] based on digital (32, 106, 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]

(106−70, 106, 48)-Net over F₃ — Digital

Digital (36, 106, 48)-net over F₃, using

net from sequence [i] based on digital (36, 47)-sequence over F₃, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 36 and N(F) ≥ 48, using
  - a curve from the manYPoints database [i]

(106−70, 106, 117)-Net in Base 3 — Upper bound on s

There is no (36, 106, 118)-net in base 3, because

1 times m-reduction [i] would yield (36, 105, 118)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹⁰⁵, 118, S₃, 69), but
  - the linear programming bound shows that MÂ â‰¥ 263 758713 430513 222927 586065 511011 987998 995736 826543 303683 / 1 764070 > 3¹⁰⁵ [i]