MinT - Best Known (14−9, 14, s)-Nets in Base 16

Best Known (14−9, 14, s)-Nets in Base 16

(14−9, 14, 49)-Net over F₁₆ — Constructive and digital

Digital (5, 14, 49)-net over F₁₆, using

net from sequence [i] based on digital (5, 48)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 5 and N(F) ≥ 49, using
  - a function field by SÃ©mirat [i]

(14−9, 14, 65)-Net in Base 16 — Constructive

(5, 14, 65)-net in base 16, using

1 times m-reduction [i] based on (5, 15, 65)-net in base 16, using
- base change [i] based on digital (0, 10, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]

(14−9, 14, 1207)-Net in Base 16 — Upper bound on s

There is no (5, 14, 1208)-net in base 16, because

1 times m-reduction [i] would yield (5, 13, 1208)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 4518 132910 804831 > 16¹³ [i]