MinT - Best Known (38, 38+61, s)-Nets in Base 32

Best Known (38, 38+61, s)-Nets in Base 32

(38, 38+61, 142)-Net over F₃₂ — Constructive and digital

Digital (38, 99, 142)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (1, 31, 44)-net over F₃₂, using
  - net from sequence [i] based on digital (1, 43)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 1 and N(F) ≥ 44, using
      - a function field by SÃ©mirat [i]
2. digital (7, 68, 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+61, 288)-Net in Base 32 — Constructive

(38, 99, 288)-net in base 32, using

32¹ times duplication [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+61, 291)-Net over F₃₂ — Digital

Digital (38, 99, 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+61, 342)-Net in Base 32

(38, 99, 342)-net in base 32, using

9 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+61, 32065)-Net in Base 32 — Upper bound on s

There is no (38, 99, 32066)-net in base 32, because

1 times m-reduction [i] would yield (38, 98, 32066)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3197 547169 360972 003740 638592 063534 990039 780579 813194 582944 699044 400135 044837 983188 407157 883494 675585 263093 565427 649326 859811 546556 737984 527732 154720 > 32⁹⁸ [i]