MinT - Best Known (103−83, 103, s)-Nets in Base 16

Best Known (103−83, 103, s)-Nets in Base 16

(103−83, 103, 65)-Net over F₁₆ — Constructive and digital

Digital (20, 103, 65)-net over F₁₆, using

t-expansion [i] based on digital (6, 103, 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]

(103−83, 103, 129)-Net over F₁₆ — Digital

Digital (20, 103, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 103, 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]

(103−83, 103, 1042)-Net in Base 16 — Upper bound on s

There is no (20, 103, 1043)-net in base 16, because

1 times m-reduction [i] would yield (20, 102, 1043)-net in base 16, but
- the generalized Rao bound for nets shows that 16^mÂ â‰¥ 671 280029 142153 208020 353838 991861 921046 693204 631242 742874 181179 304512 025631 103355 467788 496650 788326 589470 124315 545140 109696 > 16¹⁰² [i]