MinT - Best Known (49−41, 49, s)-Nets in Base 16

Best Known (49−41, 49, s)-Nets in Base 16

(49−41, 49, 65)-Net over F₁₆ — Constructive and digital

Digital (8, 49, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 49, 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]

(49−41, 49, 418)-Net in Base 16 — Upper bound on s

There is no (8, 49, 419)-net in base 16, because

1 times m-reduction [i] would yield (8, 48, 419)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6313 862467 927333 833245 011491 755206 542573 688086 553276 507576 > 16⁴⁸ [i]