MinT - Best Known (25−15, 25, s)-Nets in Base 32

Best Known (25−15, 25, s)-Nets in Base 32

(25−15, 25, 104)-Net over F₃₂ — Constructive and digital

Digital (10, 25, 104)-net over F₃₂, using

t-expansion [i] based on digital (9, 25, 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]

(25−15, 25, 113)-Net over F₃₂ — Digital

Digital (10, 25, 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]

(25−15, 25, 257)-Net in Base 32 — Constructive

(10, 25, 257)-net in base 32, using

32¹ times duplication [i] based on (9, 24, 257)-net in base 32, using
- base change [i] based on digital (0, 15, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(25−15, 25, 15775)-Net in Base 32 — Upper bound on s

There is no (10, 25, 15776)-net in base 32, because

1 times m-reduction [i] would yield (10, 24, 15776)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 329539 135029 017687 710236 214311 959513 > 32²⁴ [i]