MinT - Best Known (15, 15+59, s)-Nets in Base 32

Best Known (15, 15+59, s)-Nets in Base 32

(15, 15+59, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 74, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 74, 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]

(15, 15+59, 158)-Net over F₃₂ — Digital

Digital (15, 74, 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]

(15, 15+59, 2300)-Net in Base 32 — Upper bound on s

There is no (15, 74, 2301)-net in base 32, because

1 times m-reduction [i] would yield (15, 73, 2301)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 75 840947 112107 764797 868909 929120 699120 039797 461351 834322 830294 016311 352980 401734 144096 323481 986182 568165 535424 > 32⁷³ [i]