MinT - Best Known (62−40, 62, s)-Nets in Base 16

Best Known (62−40, 62, s)-Nets in Base 16

(62−40, 62, 65)-Net over F₁₆ — Constructive and digital

Digital (22, 62, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 62, 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]

(62−40, 62, 104)-Net in Base 16 — Constructive

(22, 62, 104)-net in base 16, using

3 times m-reduction [i] based on (22, 65, 104)-net in base 16, using
- base change [i] based on digital (9, 52, 104)-net over F₃₂, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

(62−40, 62, 129)-Net over F₁₆ — Digital

Digital (22, 62, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 62, 129)-net over F₁₆, using
- net from sequence [i] based on digital (19, 128)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 19 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(62−40, 62, 2981)-Net in Base 16 — Upper bound on s

There is no (22, 62, 2982)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 454 278324 490286 951096 526232 962946 569416 972900 292033 709264 485087 483296 059726 > 16⁶² [i]