MinT - Best Known (40, 103, s)-Nets in Base 16

Best Known (40, 103, s)-Nets in Base 16

(40, 103, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 103, 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]

(40, 103, 7566)-Net in Base 16 — Upper bound on s

There is no (40, 103, 7567)-net in base 16, because

1 times m-reduction [i] would yield (40, 102, 7567)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 661 845424 802721 383440 036663 298477 406258 784910 181087 141102 370523 737555 307828 149220 501209 522239 040295 210585 796257 379571 430656 > 16¹⁰² [i]