MinT - Best Known (21, 108, s)-Nets in Base 32

Best Known (21, 108, s)-Nets in Base 32

(21, 108, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 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]

(21, 108, 185)-Net over F₃₂ — Digital

Digital (21, 108, 185)-net over F₃₂, using

net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
  - a curve from the manYPoints database [i]

(21, 108, 3007)-Net in Base 32 — Upper bound on s

There is no (21, 108, 3008)-net in base 32, because

1 times m-reduction [i] would yield (21, 107, 3008)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112617 885991 194328 701156 660306 245698 335665 729645 734209 626973 501042 268272 894916 677755 449696 210636 511376 265593 499345 192663 436066 680896 176404 516017 039206 310943 696695 > 32¹⁰⁷ [i]