MinT - Best Known (70−35, 70, s)-Nets in Base 16

Best Known (70−35, 70, s)-Nets in Base 16

(70−35, 70, 514)-Net over F₁₆ — Constructive and digital

Digital (35, 70, 514)-net over F₁₆, using

trace code for nets [i] based on digital (0, 35, 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]

(70−35, 70, 36902)-Net in Base 16 — Upper bound on s

There is no (35, 70, 36903)-net in base 16, because

1 times m-reduction [i] would yield (35, 69, 36903)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 121439 019533 065923 060743 034596 105165 297720 018536 133950 581984 563672 629740 613763 015116 > 16⁶⁹ [i]