MinT - Best Known (38, 85, s)-Nets in Base 32

Best Known (38, 85, s)-Nets in Base 32

(38, 85, 196)-Net over F₃₂ — Constructive and digital

Digital (38, 85, 196)-net over F₃₂, using

1 times m-reduction [i] based on digital (38, 86, 196)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 31, 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, 55, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(38, 85, 288)-Net in Base 32 — Constructive

(38, 85, 288)-net in base 32, using

t-expansion [i] based on (37, 85, 288)-net in base 32, using
- 13 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
  - base change [i] based on digital (9, 70, 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]

(38, 85, 349)-Net over F₃₂ — Digital

Digital (38, 85, 349)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(38, 85, 95523)-Net in Base 32 — Upper bound on s

There is no (38, 85, 95524)-net in base 32, because

1 times m-reduction [i] would yield (38, 84, 95524)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 707944 460018 016656 881189 887087 707487 869771 484445 313185 173705 573096 817169 530839 895649 128024 613903 251958 779527 801454 586942 751848 > 32⁸⁴ [i]