MinT - Best Known (6, 6+42, s)-Nets in Base 16

Best Known (6, 6+42, s)-Nets in Base 16

(6, 6+42, 65)-Net over F₁₆ — Constructive and digital

Digital (6, 48, 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+42, 314)-Net in Base 16 — Upper bound on s

There is no (6, 48, 315)-net in base 16, because

2 times m-reduction [i] would yield (6, 46, 315)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 24 726728 512693 579650 694589 507267 266161 522188 191716 002626 > 16⁴⁶ [i]