MinT - Best Known (52−37, 52, s)-Nets in Base 32

Best Known (52−37, 52, s)-Nets in Base 32

(52−37, 52, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 52, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 52, 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]

(52−37, 52, 128)-Net in Base 32 — Constructive

(15, 52, 128)-net in base 32, using

8 times m-reduction [i] based on (15, 60, 128)-net in base 32, using
- base change [i] based on digital (5, 50, 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]

(52−37, 52, 158)-Net over F₃₂ — Digital

Digital (15, 52, 158)-net over F₃₂, using

net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
  - an algebraic function field by Beelen and Pellikaan [i]

(52−37, 52, 161)-Net in Base 32

(15, 52, 161)-net in base 32, using

2 times m-reduction [i] based on (15, 54, 161)-net in base 32, using
- base change [i] based on digital (6, 45, 161)-net over F₆₄, using
  - net from sequence [i] based on digital (6, 160)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
      - a curve from the manYPoints database [i]

(52−37, 52, 4471)-Net in Base 32 — Upper bound on s

There is no (15, 52, 4472)-net in base 32, because

1 times m-reduction [i] would yield (15, 51, 4472)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 57949 798024 083103 200835 589913 919896 946826 668524 025669 426218 197425 936832 834795 > 32⁵¹ [i]