MinT - Best Known (70−47, 70, s)-Nets in Base 32

Best Known (70−47, 70, s)-Nets in Base 32

(70−47, 70, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 70, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 70, 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]

(70−47, 70, 185)-Net over F₃₂ — Digital

Digital (23, 70, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 70, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(70−47, 70, 192)-Net in Base 32 — Constructive

(23, 70, 192)-net in base 32, using

base change [i] based on digital (3, 50, 192)-net over F₁₂₈, using
- net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
    - a function field by SÃ©mirat [i]

(70−47, 70, 225)-Net in Base 32

(23, 70, 225)-net in base 32, using

8 times m-reduction [i] based on (23, 78, 225)-net in base 32, using
- base change [i] based on digital (10, 65, 225)-net over F₆₄, using
  - net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
      - a curve from the manYPoints database [i]

(70−47, 70, 9954)-Net in Base 32 — Upper bound on s

There is no (23, 70, 9955)-net in base 32, because

1 times m-reduction [i] would yield (23, 69, 9955)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 71 704329 547505 677129 953643 106495 836556 117675 578851 671642 429817 530672 078496 208179 135900 321235 108853 563616 > 32⁶⁹ [i]