MinT - Best Known (118−59, 118, s)-Nets in Base 16

Best Known (118−59, 118, s)-Nets in Base 16

(118−59, 118, 514)-Net over F₁₆ — Constructive and digital

Digital (59, 118, 514)-net over F₁₆, using

trace code for nets [i] based on digital (0, 59, 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]

(118−59, 118, 56093)-Net in Base 16 — Upper bound on s

There is no (59, 118, 56094)-net in base 16, because

1 times m-reduction [i] would yield (59, 117, 56094)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 762 535847 728291 711715 506981 608141 176630 544640 196461 990094 846973 565258 071300 975143 982302 908834 836814 883701 127201 476113 979010 383941 273823 977391 > 16¹¹⁷ [i]