MinT - Best Known (63−31, 63, s)-Nets in Base 16

Best Known (63−31, 63, s)-Nets in Base 16

(63−31, 63, 514)-Net over F₁₆ — Constructive and digital

Digital (32, 63, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (32, 64, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 32, 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]

(63−31, 63, 40608)-Net in Base 16 — Upper bound on s

There is no (32, 63, 40609)-net in base 16, because

1 times m-reduction [i] would yield (32, 62, 40609)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 452 362767 919276 059575 025834 093162 846598 533393 414843 171912 185518 992494 015776 > 16⁶² [i]