MinT - Best Known (119−59, 119, s)-Nets in Base 16

Best Known (119−59, 119, s)-Nets in Base 16

(119−59, 119, 514)-Net over F₁₆ — Constructive and digital

Digital (60, 119, 514)-net over F₁₆, using

1 times m-reduction [i] based on digital (60, 120, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 60, 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]

(119−59, 119, 61722)-Net in Base 16 — Upper bound on s

There is no (60, 119, 61723)-net in base 16, because

1 times m-reduction [i] would yield (60, 118, 61723)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 12198 937773 750875 929129 823762 301581 147090 240424 323869 316805 622119 889927 907882 052835 312557 211516 514275 316236 554116 443549 600811 633488 729773 225856 > 16¹¹⁸ [i]