MinT - Best Known (17, 46, s)-Nets in Base 3

Best Known (17, 46, s)-Nets in Base 3

(17, 46, 28)-Net over F₃ — Constructive and digital

Digital (17, 46, 28)-net over F₃, using

t-expansion [i] based on digital (15, 46, 28)-net over F₃, using
- net from sequence [i] based on digital (15, 27)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 15 and N(F) ≥ 28, using
    - an explicitly constructive algebraic function field [i]

(17, 46, 84)-Net in Base 3 — Upper bound on s

There is no (17, 46, 85)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁴⁶, 85, S₃, 29), but
- the linear programming bound shows that MÂ â‰¥ 483937 797114 469209 051703 154413 655309 919629 037250 104075 923442 729662 978285 321149 322093 071242 287130 145997 461503 932031 / 51 976594 175635 720681 271525 585431 306623 884750 854164 220196 964183 033431 579679 265834 910579 633525 > 3⁴⁶ [i]