MinT - Best Known (94−53, 94, s)-Nets in Base 16

Best Known (94−53, 94, s)-Nets in Base 16

(94−53, 94, 225)-Net over F₁₆ — Constructive and digital

Digital (41, 94, 225)-net over F₁₆, using

t-expansion [i] based on digital (40, 94, 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]

(94−53, 94, 14249)-Net in Base 16 — Upper bound on s

There is no (41, 94, 14250)-net in base 16, because

1 times m-reduction [i] would yield (41, 93, 14250)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 9620 777261 385550 887301 038801 596691 482095 984334 279518 934577 443226 039731 067281 807415 403593 917052 777570 719005 479376 > 16⁹³ [i]