MinT - Best Known (18, 18+31, s)-Nets in Base 3

Best Known (18, 18+31, s)-Nets in Base 3

(18, 18+31, 28)-Net over F₃ — Constructive and digital

Digital (18, 49, 28)-net over F₃, using

t-expansion [i] based on digital (15, 49, 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+31, 84)-Net in Base 3 — Upper bound on s

There is no (18, 49, 85)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁴⁹, 85, S₃, 31), but
- the linear programming bound shows that MÂ â‰¥ 680029 495837 431892 373726 566388 206026 660443 378717 028919 971748 021750 421500 256283 / 2 775791 539437 123450 845959 961813 360302 598435 660143 224610 > 3⁴⁹ [i]