MinT - Best Known (104−71, 104, s)-Nets in Base 32

Best Known (104−71, 104, s)-Nets in Base 32

(104−71, 104, 120)-Net over F₃₂ — Constructive and digital

Digital (33, 104, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 104, 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]

(104−71, 104, 192)-Net in Base 32 — Constructive

(33, 104, 192)-net in base 32, using

1 times m-reduction [i] based on (33, 105, 192)-net in base 32, using
- base change [i] based on digital (3, 75, 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]

(104−71, 104, 273)-Net over F₃₂ — Digital

Digital (33, 104, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 104, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(104−71, 104, 12041)-Net in Base 32 — Upper bound on s

There is no (33, 104, 12042)-net in base 32, because

1 times m-reduction [i] would yield (33, 103, 12042)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107334 080620 730087 703739 878143 592738 842424 310776 066953 546546 490147 299731 689290 781739 065536 083073 184693 618014 612130 332691 957102 141891 332356 878766 953911 656032 > 32¹⁰³ [i]