MinT - Best Known (109−85, 109, s)-Nets in Base 32

Best Known (109−85, 109, s)-Nets in Base 32

(109−85, 109, 120)-Net over F₃₂ — Constructive and digital

Digital (24, 109, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 109, 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]

(109−85, 109, 128)-Net in Base 32 — Constructive

(24, 109, 128)-net in base 32, using

32¹ times duplication [i] based on (23, 108, 128)-net in base 32, using
- base change [i] based on digital (5, 90, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(109−85, 109, 225)-Net over F₃₂ — Digital

Digital (24, 109, 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]

(109−85, 109, 3930)-Net in Base 32 — Upper bound on s

There is no (24, 109, 3931)-net in base 32, because

1 times m-reduction [i] would yield (24, 108, 3931)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 627857 270253 574598 071838 212357 134609 931589 013487 657982 024092 532713 338394 031426 395702 248812 152582 220657 946526 943402 642477 506853 330664 832365 120566 850631 618683 247470 > 32¹⁰⁸ [i]