MinT - Best Known (16, 57, s)-Nets in Base 32

Best Known (16, 57, s)-Nets in Base 32

(16, 57, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 57, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 57, 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]

(16, 57, 128)-Net in Base 32 — Constructive

(16, 57, 128)-net in base 32, using

9 times m-reduction [i] based on (16, 66, 128)-net in base 32, using
- base change [i] based on digital (5, 55, 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]

(16, 57, 158)-Net over F₃₂ — Digital

Digital (16, 57, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 57, 158)-net over F₃₂, using
- net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
    - an algebraic function field by Beelen and Pellikaan [i]

(16, 57, 161)-Net in Base 32

(16, 57, 161)-net in base 32, using

3 times m-reduction [i] based on (16, 60, 161)-net in base 32, using
- base change [i] based on digital (6, 50, 161)-net over F₆₄, using
  - net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
      - a curve from the manYPoints database [i]

(16, 57, 4378)-Net in Base 32 — Upper bound on s

There is no (16, 57, 4379)-net in base 32, because

1 times m-reduction [i] would yield (16, 56, 4379)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 944006 908158 153401 182694 083621 018237 400989 566986 258889 620890 388928 918010 170642 339766 > 32⁵⁶ [i]