MinT - Best Known (21, 21+65, s)-Nets in Base 32

Best Known (21, 21+65, s)-Nets in Base 32

(21, 21+65, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 86, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 86, 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+65, 128)-Net in Base 32 — Constructive

(21, 86, 128)-net in base 32, using

10 times m-reduction [i] based on (21, 96, 128)-net in base 32, using
- base change [i] based on digital (5, 80, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(21, 21+65, 185)-Net over F₃₂ — Digital

Digital (21, 86, 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+65, 4090)-Net in Base 32 — Upper bound on s

There is no (21, 86, 4091)-net in base 32, because

1 times m-reduction [i] would yield (21, 85, 4091)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 86 685253 857168 948644 295960 966402 352437 833031 948985 174534 894340 522046 920895 062714 629095 626264 571057 089020 145194 560230 132000 863545 > 32⁸⁵ [i]