MinT - Best Known (40, 40+59, s)-Nets in Base 16

Best Known (40, 40+59, s)-Nets in Base 16

(40, 40+59, 225)-Net over F₁₆ — Constructive and digital

Digital (40, 99, 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, 40+59, 9106)-Net in Base 16 — Upper bound on s

There is no (40, 99, 9107)-net in base 16, because

1 times m-reduction [i] would yield (40, 98, 9107)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 10092 495572 444711 298021 690504 606349 401545 659299 483888 809047 455740 009352 634447 575669 044495 849647 937805 978774 460350 172096 > 16⁹⁸ [i]