MinT - Best Known (12, 12+18, s)-Nets in Base 32

Best Known (12, 12+18, s)-Nets in Base 32

(12, 12+18, 120)-Net over F₃₂ — Constructive and digital

Digital (12, 30, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 30, 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]

(12, 12+18, 129)-Net over F₃₂ — Digital

Digital (12, 30, 129)-net over F₃₂, using

net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
  - a curve from the manYPoints database [i]

(12, 12+18, 257)-Net in Base 32 — Constructive

(12, 30, 257)-net in base 32, using

2 times m-reduction [i] based on (12, 32, 257)-net in base 32, using
- base change [i] based on digital (0, 20, 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]

(12, 12+18, 13913)-Net in Base 32 — Upper bound on s

There is no (12, 30, 13914)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1428 121447 014312 300003 398377 688475 890293 848713 > 32³⁰ [i]