MinT - Best Known (69−46, 69, s)-Nets in Base 3

Best Known (69−46, 69, s)-Nets in Base 3

(69−46, 69, 32)-Net over F₃ — Constructive and digital

Digital (23, 69, 32)-net over F₃, using

t-expansion [i] based on digital (21, 69, 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]

(69−46, 69, 79)-Net in Base 3 — Upper bound on s

There is no (23, 69, 80)-net in base 3, because

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]