MinT - Best Known (62−26, 62, s)-Nets in Base 32

Best Known (62−26, 62, s)-Nets in Base 32

(62−26, 62, 240)-Net over F₃₂ — Constructive and digital

Digital (36, 62, 240)-net over F₃₂, using

2 times m-reduction [i] based on digital (36, 64, 240)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (11, 25, 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, 39, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂ (see above)

(62−26, 62, 407)-Net in Base 32 — Constructive

(36, 62, 407)-net in base 32, using

(u,Â u+v)-construction [i] based on
1. (7, 20, 150)-net in base 32, using
  - 1 times m-reduction [i] based on (7, 21, 150)-net in base 32, using
    - base change [i] based on digital (1, 15, 150)-net over F₁₂₈, using
      - net from sequence [i] based on digital (1, 149)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 1 and N(F) ≥ 150, using
        a function field by SÃ©mirat [i]
2. (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]

(62−26, 62, 1787)-Net over F₃₂ — Digital

Digital (36, 62, 1787)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(62−26, 62, 2757090)-Net in Base 32 — Upper bound on s

There is no (36, 62, 2757091)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2085 927243 021174 842631 092905 699786 479864 657117 999458 542068 920332 871934 355991 389358 457773 098512 > 32⁶² [i]