MinT - Best Known (15, 15+89, s)-Nets in Base 32

Best Known (15, 15+89, s)-Nets in Base 32

(15, 15+89, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 104, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 104, 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+89, 158)-Net over F₃₂ — Digital

Digital (15, 104, 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+89, 1834)-Net in Base 32 — Upper bound on s

There is no (15, 104, 1835)-net in base 32, because

1 times m-reduction [i] would yield (15, 103, 1835)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107616 192259 942467 463023 885851 788243 364519 360121 316172 419195 471244 790213 680595 191916 717999 769653 999486 824317 327223 490191 056628 003876 972891 060916 182442 246720 > 32¹⁰³ [i]