MinT - Best Known (74−50, 74, s)-Nets in Base 3

Best Known (74−50, 74, s)-Nets in Base 3

(74−50, 74, 32)-Net over F₃ — Constructive and digital

Digital (24, 74, 32)-net over F₃, using

t-expansion [i] based on digital (21, 74, 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]

(74−50, 74, 81)-Net in Base 3 — Upper bound on s

There is no (24, 74, 82)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁷⁴, 82, S₃, 50), but
- the linear programming bound shows that MÂ â‰¥ 1133 201025 509985 412089 971278 248938 614941 / 5015 > 3⁷⁴ [i]