MinT - Best Known (18−15, 18, s)-Nets in Base 16

Best Known (18−15, 18, s)-Nets in Base 16

(18−15, 18, 38)-Net over F₁₆ — Constructive and digital

Digital (3, 18, 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]

(18−15, 18, 185)-Net in Base 16 — Upper bound on s

There is no (3, 18, 186)-net in base 16, because

1 times m-reduction [i] would yield (3, 17, 186)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 296 922658 156912 900756 > 16¹⁷ [i]