MinT - Best Known (80−57, 80, s)-Nets in Base 32

Best Known (80−57, 80, s)-Nets in Base 32

(80−57, 80, 120)-Net over F₃₂ — Constructive and digital

Digital (23, 80, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 80, 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]

(80−57, 80, 177)-Net in Base 32 — Constructive

(23, 80, 177)-net in base 32, using

16 times m-reduction [i] based on (23, 96, 177)-net in base 32, using
- base change [i] based on digital (7, 80, 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]

(80−57, 80, 185)-Net over F₃₂ — Digital

Digital (23, 80, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 80, 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]

(80−57, 80, 209)-Net in Base 32

(23, 80, 209)-net in base 32, using

4 times m-reduction [i] based on (23, 84, 209)-net in base 32, using
- base change [i] based on digital (9, 70, 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]

(80−57, 80, 6417)-Net in Base 32 — Upper bound on s

There is no (23, 80, 6418)-net in base 32, because

1 times m-reduction [i] would yield (23, 79, 6418)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 80988 738125 966879 093130 552895 213087 225272 631389 370751 079682 594800 464799 330451 817501 229529 381781 198383 545322 445394 407104 > 32⁷⁹ [i]