MinT - Best Known (34, 157, s)-Nets in Base 3

Best Known (34, 157, s)-Nets in Base 3

(34, 157, 38)-Net over F₃ — Constructive and digital

Digital (34, 157, 38)-net over F₃, using

t-expansion [i] based on digital (32, 157, 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]

(34, 157, 46)-Net over F₃ — Digital

Digital (34, 157, 46)-net over F₃, using

t-expansion [i] based on digital (33, 157, 46)-net over F₃, using
- net from sequence [i] based on digital (33, 45)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 33 and N(F) ≥ 46, using
    - a curve from the manYPoints database [i]

(34, 157, 111)-Net in Base 3 — Upper bound on s

There is no (34, 157, 112)-net in base 3, because

57 times m-reduction [i] would yield (34, 100, 112)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3¹⁰⁰, 112, S₃, 66), but
  - the linear programming bound shows that MÂ â‰¥ 337012 060714 431725 512045 406748 426703 296453 236034 239913 / 541025 > 3¹⁰⁰ [i]