MinT - Best Known (24, 24+45, s)-Nets in Base 3

Best Known (24, 24+45, s)-Nets in Base 3

(24, 24+45, 32)-Net over F₃ — Constructive and digital

Digital (24, 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]

(24, 24+45, 86)-Net in Base 3 — Upper bound on s

There is no (24, 69, 87)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁶⁹, 87, S₃, 45), but
- the linear programming bound shows that MÂ â‰¥ 60 677445 989371 388018 255266 871453 026648 079313 / 55230 725056 > 3⁶⁹ [i]