MinT - Best Known (21, 21+47, s)-Nets in Base 32

Best Known (21, 21+47, s)-Nets in Base 32

(21, 21+47, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 68, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 68, 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+47, 177)-Net in Base 32 — Constructive

(21, 68, 177)-net in base 32, using

16 times m-reduction [i] based on (21, 84, 177)-net in base 32, using
- base change [i] based on digital (7, 70, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(21, 21+47, 185)-Net over F₃₂ — Digital

Digital (21, 68, 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+47, 209)-Net in Base 32

(21, 68, 209)-net in base 32, using

4 times m-reduction [i] based on (21, 72, 209)-net in base 32, using
- base change [i] based on digital (9, 60, 209)-net over F₆₄, using
  - net from sequence [i] based on digital (9, 208)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 9 and N(F) ≥ 209, using
      - a curve from the manYPoints database [i]

(21, 21+47, 7361)-Net in Base 32 — Upper bound on s

There is no (21, 68, 7362)-net in base 32, because

1 times m-reduction [i] would yield (21, 67, 7362)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 70087 638692 927524 996539 275528 822564 551197 650175 657516 528532 491351 067983 086110 157808 506579 034205 067360 > 32⁶⁷ [i]