MinT - Best Known (109−69, 109, s)-Nets in Base 16

Best Known (109−69, 109, s)-Nets in Base 16

(109−69, 109, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 109, 225)-net over F₁₆, using

net from sequence [i] based on digital (40, 224)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 40 and N(F) ≥ 225, using
  - a function field by GarcÃa and Quoos [i]

(109−69, 109, 6010)-Net in Base 16 — Upper bound on s

There is no (40, 109, 6011)-net in base 16, because

1 times m-reduction [i] would yield (40, 108, 6011)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 11146 017338 164211 483804 221262 204101 924936 786604 034869 290389 270958 660778 589682 420663 201658 995370 643990 227574 719267 990519 242595 649961 > 16¹⁰⁸ [i]