MinT - Best Known (4, 4+34, s)-Nets in Base 16

Best Known (4, 4+34, s)-Nets in Base 16

(4, 4+34, 45)-Net over F₁₆ — Constructive and digital

Digital (4, 38, 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]

(4, 4+34, 211)-Net in Base 16 — Upper bound on s

There is no (4, 38, 212)-net in base 16, because

1 times m-reduction [i] would yield (4, 37, 212)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16³⁷, 212, S₁₆, 33), but
  - the linear programming bound shows that MÂ â‰¥ 1 547409 487131 714899 677390 885780 847200 380117 291059 645539 158964 829585 839627 436032 / 4303 201222 842834 783226 830613 131997 > 16³⁷ [i]