MinT - Best Known (3, 3+30, s)-Nets in Base 16

Best Known (3, 3+30, s)-Nets in Base 16

(3, 3+30, 38)-Net over F₁₆ — Constructive and digital

Digital (3, 33, 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+30, 164)-Net in Base 16 — Upper bound on s

There is no (3, 33, 165)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16³³, 165, S₁₆, 30), but
- the linear programming bound shows that MÂ â‰¥ 5510 151213 195982 909812 215179 795185 969235 758163 245106 465135 919104 / 1 001889 792151 448962 306579 > 16³³ [i]