MinT - Best Known (6, 6+13, s)-Nets in Base 16

Best Known (6, 6+13, s)-Nets in Base 16

(6, 6+13, 65)-Net over F₁₆ — Constructive and digital

Digital (6, 19, 65)-net over F₁₆, using

net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
  - the Hermitian function field over F₁₆ [i]

(6, 6+13, 814)-Net in Base 16 — Upper bound on s

There is no (6, 19, 815)-net in base 16, because

1 times m-reduction [i] would yield (6, 18, 815)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 4735 943135 263418 990851 > 16¹⁸ [i]