MinT - Best Known (21, 21+72, s)-Nets in Base 32

Best Known (21, 21+72, s)-Nets in Base 32

(21, 21+72, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 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]

(21, 21+72, 128)-Net in Base 32 — Constructive

(21, 93, 128)-net in base 32, using

3 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+72, 185)-Net over F₃₂ — Digital

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]

(21, 21+72, 3543)-Net in Base 32 — Upper bound on s

There is no (21, 93, 3544)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 96 001246 026217 830539 537815 029613 277215 610887 734300 439058 893150 472281 314449 606906 965523 207379 728858 386458 737949 410182 167309 945757 000335 551090 > 32⁹³ [i]