MinT - Best Known (43−29, 43, s)-Nets in Base 16

Best Known (43−29, 43, s)-Nets in Base 16

(43−29, 43, 65)-Net over F₁₆ — Constructive and digital

Digital (14, 43, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 43, 65)-net over F₁₆, using
- net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
    - the Hermitian function field over F₁₆ [i]

(43−29, 43, 76)-Net in Base 16 — Constructive

(14, 43, 76)-net in base 16, using

2 times m-reduction [i] based on (14, 45, 76)-net in base 16, using
- base change [i] based on digital (5, 36, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(43−29, 43, 97)-Net over F₁₆ — Digital

Digital (14, 43, 97)-net over F₁₆, using

t-expansion [i] based on digital (13, 43, 97)-net over F₁₆, using
- net from sequence [i] based on digital (13, 96)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 13 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(43−29, 43, 1643)-Net in Base 16 — Upper bound on s

There is no (14, 43, 1644)-net in base 16, because

1 times m-reduction [i] would yield (14, 42, 1644)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 375 743453 062506 728003 091964 161932 069754 221883 018616 > 16⁴² [i]