MinT - Best Known (41, 41+53, s)-Nets in Base 32

Best Known (41, 41+53, s)-Nets in Base 32

(41, 41+53, 196)-Net over F₃₂ — Constructive and digital

Digital (41, 94, 196)-net over F₃₂, using

1 times m-reduction [i] based on digital (41, 95, 196)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 34, 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, 61, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(41, 41+53, 288)-Net in Base 32 — Constructive

(41, 94, 288)-net in base 32, using

t-expansion [i] based on (40, 94, 288)-net in base 32, using
- 14 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+53, 336)-Net over F₃₂ — Digital

Digital (41, 94, 336)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(41, 41+53, 408)-Net in Base 32

(41, 94, 408)-net in base 32, using

2 times m-reduction [i] based on (41, 96, 408)-net in base 32, using
- base change [i] based on digital (25, 80, 408)-net over F₆₄, using
  - net from sequence [i] based on digital (25, 407)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 25 and N(F) ≥ 408, using
      - a curve from the manYPoints database [i]

(41, 41+53, 82350)-Net in Base 32 — Upper bound on s

There is no (41, 94, 82351)-net in base 32, because

1 times m-reduction [i] would yield (41, 93, 82351)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 95 280617 126438 384270 836144 821851 436666 095196 209780 053967 495252 552809 687289 583618 538494 490313 679068 374229 068908 647468 541607 989084 782858 518882 > 32⁹³ [i]