MinT - Best Known (20, 48, s)-Nets in Base 16

Best Known (20, 48, s)-Nets in Base 16

(20, 48, 82)-Net over F₁₆ — Constructive and digital

Digital (20, 48, 82)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (0, 14, 17)-net over F₁₆, using
  - net from sequence [i] based on digital (0, 16)-sequence over F₁₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 0 and N(F) ≥ 17, using
      - the rational function field F₁₆(x) [i]
    - Niederreiter sequence [i]
2. digital (6, 34, 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]

(20, 48, 104)-Net in Base 16 — Constructive

(20, 48, 104)-net in base 16, using

7 times m-reduction [i] based on (20, 55, 104)-net in base 16, using
- base change [i] based on digital (9, 44, 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]

(20, 48, 129)-Net over F₁₆ — Digital

Digital (20, 48, 129)-net over F₁₆, using

t-expansion [i] based on digital (19, 48, 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]

(20, 48, 5409)-Net in Base 16 — Upper bound on s

There is no (20, 48, 5410)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 6280 241011 684444 214122 223712 001188 687872 343009 140478 420976 > 16⁴⁸ [i]