MinT - Best Known (45, 45+45, s)-Nets in Base 16

Best Known (45, 45+45, s)-Nets in Base 16

(45, 45+45, 514)-Net over F₁₆ — Constructive and digital

Digital (45, 90, 514)-net over F₁₆, using

trace code for nets [i] based on digital (0, 45, 257)-net over F₂₅₆, using
- net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
    - the rational function field F₂₅₆(x) [i]
  - Niederreiter sequence [i]

(45, 45+45, 44859)-Net in Base 16 — Upper bound on s

There is no (45, 90, 44860)-net in base 16, because

1 times m-reduction [i] would yield (45, 89, 44860)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 146788 904668 421611 606239 539402 767209 169195 850612 703481 259899 575591 690446 463431 196763 352372 158147 180717 154926 > 16⁸⁹ [i]