MinT - Best Known (91−45, 91, s)-Nets in Base 16

Best Known (91−45, 91, s)-Nets in Base 16

(91−45, 91, 514)-Net over F₁₆ — Constructive and digital

Digital (46, 91, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (46, 92, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 46, 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]

(91−45, 91, 50886)-Net in Base 16 — Upper bound on s

There is no (46, 91, 50887)-net in base 16, because

1 times m-reduction [i] would yield (46, 90, 50887)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 2 348757 682493 321575 862737 869252 559568 671042 682135 803691 387565 690272 930109 883922 124957 793104 733177 106069 833636 > 16⁹⁰ [i]