MinT - Best Known (3, 3+69, s)-Nets in Base 16

Best Known (3, 3+69, s)-Nets in Base 16

(3, 3+69, 38)-Net over F₁₆ — Constructive and digital

Digital (3, 72, 38)-net over F₁₆, using

net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
  - a function field by SÃ©mirat [i]

(3, 3+69, 64)-Net in Base 16 — Upper bound on s

There is no (3, 72, 65)-net in base 16, because

11 times m-reduction [i] would yield (3, 61, 65)-net in base 16, but
- extracting embedded orthogonal array [i] would yield OA(16⁶¹, 65, S₁₆, 58), but
  - the linear programming bound shows that MÂ â‰¥ 159214 122701 309768 707410 104386 945873 298246 228915 255775 554254 178010 880553 254912 / 5487 > 16⁶¹ [i]