MinT - Best Known (41−38, 41, s)-Nets in Base 16

Best Known (41−38, 41, s)-Nets in Base 16

(41−38, 41, 38)-Net over F₁₆ — Constructive and digital

Digital (3, 41, 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]

(41−38, 41, 151)-Net in Base 16 — Upper bound on s

There is no (3, 41, 152)-net in base 16, because

extracting embedded orthogonal array [i] would yield OA(16⁴¹, 152, S₁₆, 38), but
- the linear programming bound shows that MÂ â‰¥ 32 860194 755523 301187 210271 189805 437301 285421 870757 651276 700582 196029 685760 / 1 382617 959177 130849 930699 > 16⁴¹ [i]