MinT - Best Known (22, 22+71, s)-Nets in Base 32

Best Known (22, 22+71, s)-Nets in Base 32

(22, 22+71, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 93, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 93, 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]

(22, 22+71, 128)-Net in Base 32 — Constructive

(22, 93, 128)-net in base 32, using

9 times m-reduction [i] based on (22, 102, 128)-net in base 32, using
- base change [i] based on digital (5, 85, 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]

(22, 22+71, 185)-Net over F₃₂ — Digital

Digital (22, 93, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 93, 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]

(22, 22+71, 4039)-Net in Base 32 — Upper bound on s

There is no (22, 93, 4040)-net in base 32, because

1 times m-reduction [i] would yield (22, 92, 4040)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 983775 468435 075730 648890 515595 621130 912220 389025 942168 995345 939883 529879 865897 516499 026381 203364 214001 982091 881643 600139 197060 775358 649394 > 32⁹² [i]