MinT - Best Known (70−47, 70, s)-Nets in Base 3

Best Known (70−47, 70, s)-Nets in Base 3

(70−47, 70, 32)-Net over F₃ — Constructive and digital

Digital (23, 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]

(70−47, 70, 79)-Net in Base 3 — Upper bound on s

There is no (23, 70, 80)-net in base 3, because

1 times m-reduction [i] would yield (23, 69, 80)-net in base 3, but
- extracting embedded orthogonal array [i] would yield OA(3⁶⁹, 80, S₃, 46), but
  - the linear programming bound shows that MÂ â‰¥ 904 357542 932493 278414 499056 136998 127663 / 977647 > 3⁶⁹ [i]