MinT - Best Known (17, 17+43, s)-Nets in Base 32

Best Known (17, 17+43, s)-Nets in Base 32

(17, 17+43, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 60, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 60, 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, 17+43, 158)-Net over F₃₂ — Digital

Digital (17, 60, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 60, 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, 17+43, 177)-Net in Base 32 — Constructive

(17, 60, 177)-net in base 32, using

base change [i] based on digital (7, 50, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(17, 17+43, 4730)-Net in Base 32 — Upper bound on s

There is no (17, 60, 4731)-net in base 32, because

1 times m-reduction [i] would yield (17, 59, 4731)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 63798 945245 776978 656573 192835 618896 018386 230925 383648 938112 473457 263584 189828 320746 030996 > 32⁵⁹ [i]