MinT - Best Known (50−36, 50, s)-Nets in Base 32

Best Known (50−36, 50, s)-Nets in Base 32

(50−36, 50, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 50, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 50, 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]

(50−36, 50, 128)-Net in Base 32 — Constructive

(14, 50, 128)-net in base 32, using

4 times m-reduction [i] based on (14, 54, 128)-net in base 32, using
- base change [i] based on digital (5, 45, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(50−36, 50, 146)-Net over F₃₂ — Digital

Digital (14, 50, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(50−36, 50, 3686)-Net in Base 32 — Upper bound on s

There is no (14, 50, 3687)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1809 275701 745259 596812 649821 040352 118973 761978 283157 809557 124943 939829 000790 > 32⁵⁰ [i]