MinT - Best Known (91−53, 91, s)-Nets in Base 32

Best Known (91−53, 91, s)-Nets in Base 32

(91−53, 91, 174)-Net over F₃₂ — Constructive and digital

Digital (38, 91, 174)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 31, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]
2. digital (7, 60, 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]

(91−53, 91, 288)-Net in Base 32 — Constructive

(38, 91, 288)-net in base 32, using

t-expansion [i] based on (37, 91, 288)-net in base 32, using
- 7 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]

(91−53, 91, 291)-Net over F₃₂ — Digital

Digital (38, 91, 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]

(91−53, 91, 342)-Net in Base 32

(38, 91, 342)-net in base 32, using

17 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]

(91−53, 91, 55202)-Net in Base 32 — Upper bound on s

There is no (38, 91, 55203)-net in base 32, because

1 times m-reduction [i] would yield (38, 90, 55203)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2907 653325 578669 418055 453904 877592 029171 823017 225442 259895 724334 889051 398248 197840 050186 262400 891673 585062 895394 079610 527527 073774 247260 > 32⁹⁰ [i]