MinT - Best Known (36−31, 36, s)-Nets in Base 16

Best Known (36−31, 36, s)-Nets in Base 16

(36−31, 36, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 36, 49)-net over F₁₆, using

net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
  - a function field by SÃ©mirat [i]

(36−31, 36, 268)-Net in Base 16 — Upper bound on s

There is no (5, 36, 269)-net in base 16, because

1 times m-reduction [i] would yield (5, 35, 269)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 447604 669624 647732 414728 614410 471188 011776 > 16³⁵ [i]