MinT - Best Known (105−67, 105, s)-Nets in Base 32

Best Known (105−67, 105, s)-Nets in Base 32

(105−67, 105, 120)-Net over F₃₂ — Constructive and digital

Digital (38, 105, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 105, 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]

(105−67, 105, 216)-Net in Base 32 — Constructive

(38, 105, 216)-net in base 32, using

t-expansion [i] based on (36, 105, 216)-net in base 32, using
- 3 times m-reduction [i] based on (36, 108, 216)-net in base 32, using
  - base change [i] based on (18, 90, 216)-net in base 64, using
    - 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
      - base change [i] based on digital (5, 78, 216)-net over F₁₂₈, using
        net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(105−67, 105, 291)-Net over F₃₂ — Digital

Digital (38, 105, 291)-net over F₃₂, using

net from sequence [i] based on digital (38, 290)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 38 and N(F) ≥ 291, using
  - a curve from the manYPoints database [i]

(105−67, 105, 342)-Net in Base 32

(38, 105, 342)-net in base 32, using

3 times m-reduction [i] based on (38, 108, 342)-net in base 32, using
- base change [i] based on digital (20, 90, 342)-net over F₆₄, using
  - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
      - a curve from the manYPoints database [i]

(105−67, 105, 23506)-Net in Base 32 — Upper bound on s

There is no (38, 105, 23507)-net in base 32, because

1 times m-reduction [i] would yield (38, 104, 23507)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 436817 887966 977393 585050 018436 312295 444275 810412 470136 880672 433033 683930 457272 247733 979545 560961 661154 383875 392558 024359 501499 064619 517612 607228 293673 126820 > 32¹⁰⁴ [i]