MinT - Best Known (36−20, 36, s)-Nets in Base 49

Best Known (36−20, 36, s)-Nets in Base 49

(36−20, 36, 150)-Net over F₄₉ — Constructive and digital

Digital (16, 36, 150)-net over F₄₉, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 6, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
      - the rational function field F₄₉(x) [i]
    - Niederreiter sequence [i]
2. digital (0, 10, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)
3. digital (0, 20, 50)-net over F₄₉, using
  - net from sequence [i] based on digital (0, 49)-sequence over F₄₉ (see above)

(36−20, 36, 273)-Net over F₄₉ — Digital

Digital (16, 36, 273)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(36−20, 36, 114662)-Net in Base 49 — Upper bound on s

There is no (16, 36, 114663)-net in base 49, because

the generalized Rao bound for nets shows that 49^mÂ â‰¥ 7 031705 446923 811392 141227 615996 278054 458218 161812 895942 339873 > 49³⁶ [i]