MinT - Best Known (16, 16+35, s)-Nets in Base 3

Best Known (16, 16+35, s)-Nets in Base 3

(16, 16+35, 28)-Net over F₃ — Constructive and digital

Digital (16, 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]

(16, 16+35, 57)-Net in Base 3 — Upper bound on s

There is no (16, 51, 58)-net in base 3, because

extracting embedded orthogonal array [i] would yield OA(3⁵¹, 58, S₃, 35), but
- the linear programming bound shows that MÂ â‰¥ 2151 540269 112482 208544 436253 / 946 > 3⁵¹ [i]