MinT - Best Known (46, 78, s)-Nets in Base 32

Best Known (46, 78, s)-Nets in Base 32

(46, 78, 273)-Net over F₃₂ — Constructive and digital

Digital (46, 78, 273)-net over F₃₂, using

generalized (u,Â u+v)-construction [i] based on
1. digital (6, 16, 77)-net over F₃₂, using
  - (u,Â u+v)-construction [i] based on
    1. digital (0, 5, 33)-net over F₃₂, using
      - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
        the rational function field F₃₂(x) [i]
        Niederreiter sequence [i]
    2. digital (1, 11, 44)-net over F₃₂, using
      - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
        a function field by SÃ©mirat [i]
2. digital (7, 23, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]
3. digital (7, 39, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(46, 78, 514)-Net in Base 32 — Constructive

(46, 78, 514)-net in base 32, using

base change [i] based on (33, 65, 514)-net in base 64, using
- 1 times m-reduction [i] based on (33, 66, 514)-net in base 64, using
  - (u,Â u+v)-construction [i] based on
    1. (6, 22, 257)-net in base 64, using
      - 2 times m-reduction [i] based on (6, 24, 257)-net in base 64, using
        base change [i] based on digital (0, 18, 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. (11, 44, 257)-net in base 64, using
      - base change [i] based on digital (0, 33, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(46, 78, 2469)-Net over F₃₂ — Digital

Digital (46, 78, 2469)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(46, 78, 4772901)-Net in Base 32 — Upper bound on s

There is no (46, 78, 4772902)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2521 735047 080689 768076 022524 575985 071138 925773 418182 166475 869517 237596 769125 495217 175069 142435 587284 462968 646467 249294 > 32⁷⁸ [i]