MinT - Best Known (10, 10+21, s)-Nets in Base 32

Best Known (10, 10+21, s)-Nets in Base 32

(10, 10+21, 104)-Net over F₃₂ — Constructive and digital

Digital (10, 31, 104)-net over F₃₂, using

t-expansion [i] based on digital (9, 31, 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]

(10, 10+21, 113)-Net over F₃₂ — Digital

Digital (10, 31, 113)-net over F₃₂, using

net from sequence [i] based on digital (10, 112)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 10 and N(F) ≥ 113, using
  - a curve from the manYPoints database [i]

(10, 10+21, 129)-Net in Base 32 — Constructive

(10, 31, 129)-net in base 32, using

4 times m-reduction [i] based on (10, 35, 129)-net in base 32, using
- base change [i] based on digital (0, 25, 129)-net over F₁₂₈, using
  - net from sequence [i] based on digital (0, 128)-sequence over F₁₂₈, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 0 and N(F) ≥ 129, using
      - the rational function field F₁₂₈(x) [i]
    - Niederreiter sequence [i]

(10, 10+21, 4782)-Net in Base 32 — Upper bound on s

There is no (10, 31, 4783)-net in base 32, because

1 times m-reduction [i] would yield (10, 30, 4783)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1429 661844 817339 481479 857839 922254 309034 188293 > 32³⁰ [i]