MinT - Best Known (53, 53+57, s)-Nets in Base 16

Best Known (53, 53+57, s)-Nets in Base 16

(53, 53+57, 243)-Net over F₁₆ — Constructive and digital

Digital (53, 110, 243)-net over F₁₆, using

t-expansion [i] based on digital (48, 110, 243)-net over F₁₆, using
- net from sequence [i] based on digital (48, 242)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 48 and N(F) ≥ 243, using
    - a function field by GarcÃa and Quoos [i]

(53, 53+57, 324)-Net over F₁₆ — Digital

Digital (53, 110, 324)-net over F₁₆, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+57, 36660)-Net in Base 16 — Upper bound on s

There is no (53, 110, 36661)-net in base 16, because

1 times m-reduction [i] would yield (53, 109, 36661)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 177513 120248 408885 708453 839978 475333 374436 869745 778969 618174 799476 376843 853041 282277 416719 588520 179662 146649 416264 831871 066163 921796 > 16¹⁰⁹ [i]