MinT - Best Known (35, 35+25, s)-Nets in Base 32

Best Known (35, 35+25, s)-Nets in Base 32

(35, 35+25, 240)-Net over F₃₂ — Constructive and digital

Digital (35, 60, 240)-net over F₃₂, using

1 times m-reduction [i] based on digital (35, 61, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 24, 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]
  2. digital (11, 37, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(35, 35+25, 514)-Net in Base 32 — Constructive

(35, 60, 514)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (8, 20, 257)-net in base 32, using
  - 1 times m-reduction [i] based on (8, 21, 257)-net in base 32, using
    - base change [i] based on (2, 15, 257)-net in base 128, using
      - 1 times m-reduction [i] based on (2, 16, 257)-net in base 128, using
        base change [i] based on digital (0, 14, 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]
2. (15, 40, 257)-net in base 32, using
  - base change [i] based on digital (0, 25, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(35, 35+25, 1844)-Net over F₃₂ — Digital

Digital (35, 60, 1844)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(35, 35+25, 4288642)-Net in Base 32 — Upper bound on s

There is no (35, 60, 4288643)-net in base 32, because

1 times m-reduction [i] would yield (35, 59, 4288643)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 63657 453944 431951 428466 181559 939696 925640 385092 106019 536548 146468 943143 886193 821432 964192 > 32⁵⁹ [i]