MinT - Best Known (106−81, 106, s)-Nets in Base 32

Best Known (106−81, 106, s)-Nets in Base 32

(106−81, 106, 120)-Net over F₃₂ — Constructive and digital

Digital (25, 106, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 106, 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]

(106−81, 106, 177)-Net in Base 32 — Constructive

(25, 106, 177)-net in base 32, using

2 times m-reduction [i] based on (25, 108, 177)-net in base 32, using
- base change [i] based on digital (7, 90, 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]

(106−81, 106, 225)-Net over F₃₂ — Digital

Digital (25, 106, 225)-net over F₃₂, using

t-expansion [i] based on digital (24, 106, 225)-net over F₃₂, using
- net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(106−81, 106, 4523)-Net in Base 32 — Upper bound on s

There is no (25, 106, 4524)-net in base 32, because

1 times m-reduction [i] would yield (25, 105, 4524)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 110 483883 429072 459957 988633 418574 851149 406465 711791 172314 097687 931608 171454 289324 736650 302635 239651 344299 530815 377303 291280 883214 735235 156711 608303 049570 857817 > 32¹⁰⁵ [i]