MinT - Best Known (9, 33, s)-Nets in Base 32

Best Known (9, 33, s)-Nets in Base 32

(9, 33, 104)-Net over F₃₂ — Constructive and digital

Digital (9, 33, 104)-net over F₃₂, using

net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
  - a function field by SÃ©mirat [i]

(9, 33, 108)-Net over F₃₂ — Digital

Digital (9, 33, 108)-net over F₃₂, using

net from sequence [i] based on digital (9, 107)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 108, using
  - a curve from the manYPoints database [i]

(9, 33, 113)-Net in Base 32

(9, 33, 113)-net in base 32, using

3 times m-reduction [i] based on (9, 36, 113)-net in base 32, using
- base change [i] based on digital (3, 30, 113)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 112)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
      - a curve from the manYPoints database [i]

(9, 33, 2344)-Net in Base 32 — Upper bound on s

There is no (9, 33, 2345)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 46 857265 617896 686479 693685 467505 230155 086632 132264 > 32³³ [i]