MinT - Best Known (18, 18+26, s)-Nets in Base 16

Best Known (18, 18+26, s)-Nets in Base 16

(18, 18+26, 71)-Net over F₁₆ — Constructive and digital

Digital (18, 44, 71)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (2, 15, 33)-net over F₁₆, using
  - net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
      - a function field by SÃ©mirat [i]
2. digital (3, 29, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(18, 18+26, 104)-Net in Base 16 — Constructive

(18, 44, 104)-net in base 16, using

1 times m-reduction [i] based on (18, 45, 104)-net in base 16, using
- base change [i] based on digital (9, 36, 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]

(18, 18+26, 113)-Net over F₁₆ — Digital

Digital (18, 44, 113)-net over F₁₆, using

net from sequence [i] based on digital (18, 112)-sequence over F₁₆, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 18 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(18, 18+26, 4488)-Net in Base 16 — Upper bound on s

There is no (18, 44, 4489)-net in base 16, because

the generalized Rao bound for nets shows that 16^mÂ â‰¥ 95824 606919 297316 092751 911061 292433 196889 447904 361856 > 16⁴⁴ [i]