MinT - Best Known (36−22, 36, s)-Nets in Base 32

Best Known (36−22, 36, s)-Nets in Base 32

(36−22, 36, 120)-Net over F₃₂ — Constructive and digital

Digital (14, 36, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 36, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(36−22, 36, 146)-Net over F₃₂ — Digital

Digital (14, 36, 146)-net over F₃₂, using

net from sequence [i] based on digital (14, 145)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 14 and N(F) ≥ 146, using
  - a curve from the manYPoints database [i]

(36−22, 36, 257)-Net in Base 32 — Constructive

(14, 36, 257)-net in base 32, using

base change [i] based on (8, 30, 257)-net in base 64, using
- 2 times m-reduction [i] based on (8, 32, 257)-net in base 64, using
  - base change [i] based on digital (0, 24, 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]

(36−22, 36, 13348)-Net in Base 32 — Upper bound on s

There is no (14, 36, 13349)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 533468 148730 293088 968289 503938 189316 581436 099392 090960 > 32³⁶ [i]