MinT - Best Known (95−54, 95, s)-Nets in Base 32

Best Known (95−54, 95, s)-Nets in Base 32

(95−54, 95, 196)-Net over F₃₂ — Constructive and digital

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)

(95−54, 95, 288)-Net in Base 32 — Constructive

(41, 95, 288)-net in base 32, using

t-expansion [i] based on (40, 95, 288)-net in base 32, using
- 13 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]

(95−54, 95, 323)-Net over F₃₂ — Digital

Digital (41, 95, 323)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−54, 95, 408)-Net in Base 32

(41, 95, 408)-net in base 32, using

1 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]

(95−54, 95, 69639)-Net in Base 32 — Upper bound on s

There is no (41, 95, 69640)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 97567 411150 546623 110992 839413 143584 876390 706176 735994 394275 413330 076801 375610 853244 395792 171628 738418 752823 125257 100769 966801 078705 768546 002432 > 32⁹⁵ [i]