MinT - Best Known (70−46, 70, s)-Nets in Base 3

Best Known (70−46, 70, s)-Nets in Base 3

(70−46, 70, 32)-Net over F₃ — Constructive and digital

Digital (24, 70, 32)-net over F₃, using

t-expansion [i] based on digital (21, 70, 32)-net over F₃, using
- net from sequence [i] based on digital (21, 31)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 21 and N(F) ≥ 32, using
    - an explicitly constructive algebraic function field [i]

(70−46, 70, 84)-Net in Base 3 — Upper bound on s

There is no (24, 70, 85)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁷⁰, 85, S₃, 46), but
- the linear programming bound shows that MÂ â‰¥ 640 504927 462165 667703 027244 227660 956271 / 192089 > 3⁷⁰ [i]