MinT - Best Known (96−62, 96, s)-Nets in Base 16

Best Known (96−62, 96, s)-Nets in Base 16

(96−62, 96, 65)-Net over F₁₆ — Constructive and digital

Digital (34, 96, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 96, 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]

(96−62, 96, 120)-Net in Base 16 — Constructive

(34, 96, 120)-net in base 16, using

19 times m-reduction [i] based on (34, 115, 120)-net in base 16, using
- base change [i] based on digital (11, 92, 120)-net over F₃₂, using
  - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
      - a function field by SÃ©mirat [i]

(96−62, 96, 193)-Net over F₁₆ — Digital

Digital (34, 96, 193)-net over F₁₆, using

t-expansion [i] based on digital (33, 96, 193)-net over F₁₆, using
- net from sequence [i] based on digital (33, 192)-sequence over F₁₆, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 33 and N(F) ≥ 193, using
    - a curve from the manYPoints database [i]

(96−62, 96, 4417)-Net in Base 16 — Upper bound on s

There is no (34, 96, 4418)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 39 596976 983012 046642 707129 166403 468775 628881 476125 684817 253391 931663 843502 859410 065449 665213 647759 343251 429344 126496 > 16⁹⁶ [i]