MinT - Best Known (38, 38+55, s)-Nets in Base 32

Best Known (38, 38+55, s)-Nets in Base 32

(38, 38+55, 162)-Net over F₃₂ — Constructive and digital

Digital (38, 93, 162)-net over F₃₂, using

1 times m-reduction [i] based on digital (38, 94, 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, 63, 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+55, 288)-Net in Base 32 — Constructive

(38, 93, 288)-net in base 32, using

t-expansion [i] based on (37, 93, 288)-net in base 32, using
- 5 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, 38+55, 291)-Net over F₃₂ — Digital

Digital (38, 93, 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+55, 342)-Net in Base 32

(38, 93, 342)-net in base 32, using

15 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+55, 47378)-Net in Base 32 — Upper bound on s

There is no (38, 93, 47379)-net in base 32, because

1 times m-reduction [i] would yield (38, 92, 47379)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 978751 093957 064601 388266 607607 229977 599155 831618 505779 383393 559829 015716 838272 758142 268016 662841 837362 144980 151109 093441 689426 617846 579968 > 32⁹² [i]