MinT - Best Known (17, 44, s)-Nets in Base 32

Best Known (17, 44, s)-Nets in Base 32

(17, 44, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 44, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 44, 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]

(17, 44, 158)-Net over F₃₂ — Digital

Digital (17, 44, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 44, 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]

(17, 44, 192)-Net in Base 32 — Constructive

(17, 44, 192)-net in base 32, using

5 times m-reduction [i] based on (17, 49, 192)-net in base 32, using
- base change [i] based on digital (3, 35, 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]

(17, 44, 209)-Net in Base 32

(17, 44, 209)-net in base 32, using

4 times m-reduction [i] based on (17, 48, 209)-net in base 32, using
- base change [i] based on digital (9, 40, 209)-net over F₆₄, using
  - net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
      - a curve from the manYPoints database [i]

(17, 44, 17396)-Net in Base 32 — Upper bound on s

There is no (17, 44, 17397)-net in base 32, because

1 times m-reduction [i] would yield (17, 43, 17397)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 52683 076856 059948 388428 577943 645904 403725 799576 368138 751302 076240 > 32⁴³ [i]