MinT - Best Known (89−73, 89, s)-Nets in Base 32

Best Known (89−73, 89, s)-Nets in Base 32

(89−73, 89, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 89, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 89, 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]

(89−73, 89, 158)-Net over F₃₂ — Digital

Digital (16, 89, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 89, 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]

(89−73, 89, 2182)-Net in Base 32 — Upper bound on s

There is no (16, 89, 2183)-net in base 32, because

1 times m-reduction [i] would yield (16, 88, 2183)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 865911 210183 328951 797599 500884 698376 107610 177952 190108 624187 832392 940628 088871 838268 647812 830809 741410 134583 505234 884528 526322 384068 > 32⁸⁸ [i]