MinT - Best Known (46−23, 46, s)-Nets in Base 16

Best Known (46−23, 46, s)-Nets in Base 16

(46−23, 46, 514)-Net over F₁₆ — Constructive and digital

Digital (23, 46, 514)-net over F₁₆, using

trace code for nets [i] based on digital (0, 23, 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]

(46−23, 46, 27591)-Net in Base 16 — Upper bound on s

There is no (23, 46, 27592)-net in base 16, because

1 times m-reduction [i] would yield (23, 45, 27592)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 1 532694 604712 629126 693617 021561 040611 130754 147583 836056 > 16⁴⁵ [i]