MinT - Best Known (102−42, 102, s)-Nets in Base 32

Best Known (102−42, 102, s)-Nets in Base 32

(102−42, 102, 316)-Net over F₃₂ — Constructive and digital

Digital (60, 102, 316)-net over F₃₂, using

1 times m-reduction [i] based on digital (60, 103, 316)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 21, 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]
  2. digital (7, 28, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (11, 54, 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]

(102−42, 102, 514)-Net in Base 32 — Constructive

(60, 102, 514)-net in base 32, using

base change [i] based on (43, 85, 514)-net in base 64, using
- 1 times m-reduction [i] based on (43, 86, 514)-net in base 64, using
  - (u,Â u+v)-construction [i] based on
    1. (7, 28, 257)-net in base 64, using
      - base change [i] based on digital (0, 21, 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, 58, 257)-net in base 64, using
      - 2 times m-reduction [i] based on (15, 60, 257)-net in base 64, using
        base change [i] based on digital (0, 45, 257)-net over F₂₅₆, using
        net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

(102−42, 102, 2912)-Net over F₃₂ — Digital

Digital (60, 102, 2912)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(102−42, 102, 5726094)-Net in Base 32 — Upper bound on s

There is no (60, 102, 5726095)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3351 955113 170769 204929 080713 257066 489617 039279 074403 052769 805535 402986 936585 461821 773941 621608 272196 602873 965648 295846 466102 023375 005182 995148 847825 723152 > 32¹⁰² [i]