MinT - Best Known (32, 32+39, s)-Nets in Base 32

Best Known (32, 32+39, s)-Nets in Base 32

(32, 32+39, 174)-Net over F₃₂ — Constructive and digital

Digital (32, 71, 174)-net over F₃₂, using

1 times m-reduction [i] based on digital (32, 72, 174)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (5, 25, 76)-net over F₃₂, using
    - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
        a function field by SÃ©mirat [i]
  2. digital (7, 47, 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]

(32, 32+39, 288)-Net in Base 32 — Constructive

(32, 71, 288)-net in base 32, using

t-expansion [i] based on (31, 71, 288)-net in base 32, using
- 6 times m-reduction [i] based on (31, 77, 288)-net in base 32, using
  - base change [i] based on digital (9, 55, 288)-net over F₁₂₈, using
    - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(32, 32+39, 318)-Net over F₃₂ — Digital

Digital (32, 71, 318)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(32, 32+39, 342)-Net in Base 32

(32, 71, 342)-net in base 32, using

1 times m-reduction [i] based on (32, 72, 342)-net in base 32, using
- base change [i] based on digital (20, 60, 342)-net over F₆₄, using
  - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
      - a curve from the manYPoints database [i]

(32, 32+39, 89762)-Net in Base 32 — Upper bound on s

There is no (32, 71, 89763)-net in base 32, because

1 times m-reduction [i] would yield (32, 70, 89763)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2293 564678 092596 047660 491711 302970 928518 646363 527778 641010 451108 071656 031173 402793 834697 378109 884451 661472 > 32⁷⁰ [i]