MinT - Best Known (58−29, 58, s)-Nets in Base 16

Best Known (58−29, 58, s)-Nets in Base 16

(58−29, 58, 514)-Net over F₁₆ — Constructive and digital

Digital (29, 58, 514)-net over F₁₆, using

trace code for nets [i] based on digital (0, 29, 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]

(58−29, 58, 32192)-Net in Base 16 — Upper bound on s

There is no (29, 58, 32193)-net in base 16, because

1 times m-reduction [i] would yield (29, 57, 32193)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 431 452724 636040 212218 402358 320326 653827 301883 265516 758354 434694 444256 > 16⁵⁷ [i]