MinT - Best Known (103−69, 103, s)-Nets in Base 32

Best Known (103−69, 103, s)-Nets in Base 32

(103−69, 103, 120)-Net over F₃₂ — Constructive and digital

Digital (34, 103, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 103, 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]

(103−69, 103, 192)-Net in Base 32 — Constructive

(34, 103, 192)-net in base 32, using

5 times m-reduction [i] based on (34, 108, 192)-net in base 32, using
- base change [i] based on (16, 90, 192)-net in base 64, using
  - 1 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
    - base change [i] based on digital (3, 78, 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]

(103−69, 103, 273)-Net over F₃₂ — Digital

Digital (34, 103, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 103, 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]

(103−69, 103, 14289)-Net in Base 32 — Upper bound on s

There is no (34, 103, 14290)-net in base 32, because

1 times m-reduction [i] would yield (34, 102, 14290)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3352 707758 953193 726858 428806 800529 046806 567876 742375 950844 649716 573663 613901 200440 364315 154950 219063 753852 751980 210142 191714 528428 293663 275467 151662 268112 > 32¹⁰² [i]