MinT - Best Known (95−57, 95, s)-Nets in Base 32

Best Known (95−57, 95, s)-Nets in Base 32

(95−57, 95, 162)-Net over F₃₂ — Constructive and digital

Digital (38, 95, 162)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 31, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]
2. digital (7, 64, 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]

(95−57, 95, 288)-Net in Base 32 — Constructive

(38, 95, 288)-net in base 32, using

t-expansion [i] based on (37, 95, 288)-net in base 32, using
- 3 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]

(95−57, 95, 291)-Net over F₃₂ — Digital

Digital (38, 95, 291)-net over F₃₂, using

net from sequence [i] based on digital (38, 290)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 38 and N(F) ≥ 291, using
  - a curve from the manYPoints database [i]

(95−57, 95, 342)-Net in Base 32

(38, 95, 342)-net in base 32, using

13 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
- base change [i] based on digital (20, 90, 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]

(95−57, 95, 41161)-Net in Base 32 — Upper bound on s

There is no (38, 95, 41162)-net in base 32, because

1 times m-reduction [i] would yield (38, 94, 41162)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3048 889671 766604 479448 528616 565490 557506 988934 373172 481478 069155 902811 340611 531361 100770 097055 073794 051599 694877 100299 839654 013192 648389 199120 > 32⁹⁴ [i]