MinT - Best Known (17, 17+55, s)-Nets in Base 32

Best Known (17, 17+55, s)-Nets in Base 32

(17, 17+55, 120)-Net over F₃₂ — Constructive and digital

Digital (17, 72, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 72, 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+55, 128)-Net in Base 32 — Constructive

(17, 72, 128)-net in base 32, using

base change [i] based on digital (5, 60, 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]

(17, 17+55, 158)-Net over F₃₂ — Digital

Digital (17, 72, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 72, 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+55, 3185)-Net in Base 32 — Upper bound on s

There is no (17, 72, 3186)-net in base 32, because

1 times m-reduction [i] would yield (17, 71, 3186)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 73843 358516 348284 149149 084848 219233 812240 989298 059093 238739 768120 727846 155956 588429 200885 533320 885719 130576 > 32⁷¹ [i]