MinT - Best Known (49−45, 49, s)-Nets in Base 16

Best Known (49−45, 49, s)-Nets in Base 16

(49−45, 49, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 49, 45)-net over F₁₆, using

net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
  - a function field by GarcÃa and Quoos [i]

(49−45, 49, 188)-Net in Base 16 — Upper bound on s

There is no (4, 49, 189)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁴⁹, 189, S₁₆, 45), but
- the linear programming bound shows that MÂ â‰¥ 382 016331 166260 928110 705516 215825 045593 611320 701697 171789 153751 621327 715901 164530 696192 / 3715 266944 975989 924544 521747 > 16⁴⁹ [i]