MinT - Best Known (21, 21+79, s)-Nets in Base 32

Best Known (21, 21+79, s)-Nets in Base 32

(21, 21+79, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 100, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 100, 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, 21+79, 185)-Net over F₃₂ — Digital

Digital (21, 100, 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, 21+79, 3266)-Net in Base 32 — Upper bound on s

There is no (21, 100, 3267)-net in base 32, because

1 times m-reduction [i] would yield (21, 99, 3267)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 102306 062696 888911 673522 775388 535824 309881 435815 049621 153001 137069 849135 496198 719221 343152 131188 206820 632246 426823 717267 427464 792261 840970 279935 007424 > 32⁹⁹ [i]