MinT - Best Known (36, 36+60, s)-Nets in Base 32

Best Known (36, 36+60, s)-Nets in Base 32

(36, 36+60, 128)-Net over F₃₂ — Constructive and digital

Digital (36, 96, 128)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (3, 33, 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 (3, 63, 64)-net over F₃₂, using
  - net from sequence [i] based on digital (3, 63)-sequence over F₃₂ (see above)

(36, 36+60, 257)-Net in Base 32 — Constructive

(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]

(36, 36+60, 273)-Net over F₃₂ — Digital

Digital (36, 96, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 96, 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]

(36, 36+60, 342)-Net in Base 32

(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]

(36, 36+60, 25447)-Net in Base 32 — Upper bound on s

There is no (36, 96, 25448)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 124036 709071 302341 588623 995583 907352 249495 002881 245055 375102 945829 259936 096721 804075 118467 203370 298531 812833 202532 280565 480524 666377 054419 412484 > 32⁹⁶ [i]