MinT - Best Known (18, 18+33, s)-Nets in Base 3

Best Known (18, 18+33, s)-Nets in Base 3

(18, 18+33, 28)-Net over F₃ — Constructive and digital

Digital (18, 51, 28)-net over F₃, using

t-expansion [i] based on digital (15, 51, 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]

(18, 18+33, 73)-Net in Base 3 — Upper bound on s

There is no (18, 51, 74)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵¹, 74, S₃, 33), but
- the linear programming bound shows that MÂ â‰¥ 123 263670 768810 287673 347725 757839 680807 / 56 048467 475000 > 3⁵¹ [i]