MinT - Best Known (66−41, 66, s)-Nets in Base 32

Best Known (66−41, 66, s)-Nets in Base 32

(66−41, 66, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 66, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 66, 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]

(66−41, 66, 225)-Net over F₃₂ — Digital

Digital (25, 66, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 66, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(66−41, 66, 257)-Net in Base 32 — Constructive

(25, 66, 257)-net in base 32, using

base change [i] based on (14, 55, 257)-net in base 64, using
- 1 times m-reduction [i] based on (14, 56, 257)-net in base 64, using
  - base change [i] based on digital (0, 42, 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]

(66−41, 66, 20867)-Net in Base 32 — Upper bound on s

There is no (25, 66, 20868)-net in base 32, because

1 times m-reduction [i] would yield (25, 65, 20868)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 68 382828 248451 222484 783412 786264 482175 779528 941571 298543 108148 651793 688801 321406 838206 818641 684192 > 32⁶⁵ [i]