MinT - Best Known (41−25, 41, s)-Nets in Base 32

Best Known (41−25, 41, s)-Nets in Base 32

(41−25, 41, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 41, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 41, 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]

(41−25, 41, 158)-Net over F₃₂ — Digital

Digital (16, 41, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 41, 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]

(41−25, 41, 257)-Net in Base 32 — Constructive

(16, 41, 257)-net in base 32, using

1 times m-reduction [i] based on (16, 42, 257)-net in base 32, using
- base change [i] based on (9, 35, 257)-net in base 64, using
  - 1 times m-reduction [i] based on (9, 36, 257)-net in base 64, using
    - base change [i] based on digital (0, 27, 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]

(41−25, 41, 17742)-Net in Base 32 — Upper bound on s

There is no (16, 41, 17743)-net in base 32, because

1 times m-reduction [i] would yield (16, 40, 17743)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 607151 243606 597772 070378 897181 106373 696218 320730 396604 600307 > 32⁴⁰ [i]