MinT - Best Known (93−57, 93, s)-Nets in Base 32

Best Known (93−57, 93, s)-Nets in Base 32

(93−57, 93, 142)-Net over F₃₂ — Constructive and digital

Digital (36, 93, 142)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (1, 29, 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, 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]

(93−57, 93, 257)-Net in Base 32 — Constructive

(36, 93, 257)-net in base 32, using

3 times m-reduction [i] based on (36, 96, 257)-net in base 32, using
- base change [i] based on digital (0, 60, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(93−57, 93, 273)-Net over F₃₂ — Digital

Digital (36, 93, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 93, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(93−57, 93, 342)-Net in Base 32

(36, 93, 342)-net in base 32, using

3 times m-reduction [i] based on (36, 96, 342)-net in base 32, using
- base change [i] based on digital (20, 80, 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]

(93−57, 93, 32132)-Net in Base 32 — Upper bound on s

There is no (36, 93, 32133)-net in base 32, because

1 times m-reduction [i] would yield (36, 92, 32133)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 979004 824973 844955 524927 193109 577747 517297 857688 950499 983907 573997 593155 315013 471707 839121 827631 520678 219939 132867 247993 119300 081893 764816 > 32⁹² [i]