MinT - Best Known (38, 38+62, s)-Nets in Base 32

Best Known (38, 38+62, s)-Nets in Base 32

(38, 38+62, 131)-Net over F₃₂ — Constructive and digital

Digital (38, 100, 131)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (0, 31, 33)-net over F₃₂, using
  - net from sequence [i] based on digital (0, 32)-sequence over F₃₂, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 0 and N(F) ≥ 33, using
      - the rational function field F₃₂(x) [i]
    - Niederreiter sequence [i]
2. digital (7, 69, 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]

(38, 38+62, 216)-Net in Base 32 — Constructive

(38, 100, 216)-net in base 32, using

t-expansion [i] based on (36, 100, 216)-net in base 32, using
- 8 times m-reduction [i] based on (36, 108, 216)-net in base 32, using
  - base change [i] based on (18, 90, 216)-net in base 64, using
    - 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
      - base change [i] based on digital (5, 78, 216)-net over F₁₂₈, using
        net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(38, 38+62, 291)-Net over F₃₂ — Digital

Digital (38, 100, 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]

(38, 38+62, 342)-Net in Base 32

(38, 100, 342)-net in base 32, using

8 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]

(38, 38+62, 28691)-Net in Base 32 — Upper bound on s

There is no (38, 100, 28692)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 275524 847003 067221 790209 286957 214535 159690 885513 761613 260688 562134 258110 622469 159733 831103 948788 786198 502077 984094 732470 938952 151438 105411 126025 159680 > 32¹⁰⁰ [i]