MinT - Best Known (41, 41+48, s)-Nets in Base 32

Best Known (41, 41+48, s)-Nets in Base 32

(41, 41+48, 202)-Net over F₃₂ — Constructive and digital

Digital (41, 89, 202)-net over F₃₂, using

2 times m-reduction [i] based on digital (41, 91, 202)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 32, 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 (9, 59, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]

(41, 41+48, 288)-Net in Base 32 — Constructive

(41, 89, 288)-net in base 32, using

t-expansion [i] based on (40, 89, 288)-net in base 32, using
- 19 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
  - base change [i] based on (22, 90, 288)-net in base 64, using
    - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
      - base change [i] based on digital (9, 78, 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]

(41, 41+48, 421)-Net over F₃₂ — Digital

Digital (41, 89, 421)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(41, 41+48, 425)-Net in Base 32

(41, 89, 425)-net in base 32, using

1 times m-reduction [i] based on (41, 90, 425)-net in base 32, using
- base change [i] based on digital (26, 75, 425)-net over F₆₄, using
  - net from sequence [i] based on digital (26, 424)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 26 and N(F) ≥ 425, using
      - a curve from the manYPoints database [i]

(41, 41+48, 120657)-Net in Base 32 — Upper bound on s

There is no (41, 89, 120658)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 90 861969 787964 046624 070808 933722 953241 942932 705416 751685 166855 906954 267240 374537 396917 720397 223244 536659 860926 638552 063191 086992 952072 > 32⁸⁹ [i]