MinT - Best Known (29, 29+75, s)-Nets in Base 32

Best Known (29, 29+75, s)-Nets in Base 32

(29, 29+75, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 104, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 104, 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]

(29, 29+75, 177)-Net in Base 32 — Constructive

(29, 104, 177)-net in base 32, using

t-expansion [i] based on (25, 104, 177)-net in base 32, using
- 4 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]

(29, 29+75, 257)-Net over F₃₂ — Digital

Digital (29, 104, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 104, 257)-net over F₃₂, using
- net from sequence [i] based on digital (28, 256)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 28 and N(F) ≥ 257, using
    - a curve from the manYPoints database [i]

(29, 29+75, 7301)-Net in Base 32 — Upper bound on s

There is no (29, 104, 7302)-net in base 32, because

1 times m-reduction [i] would yield (29, 103, 7302)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 107436 522173 379087 743992 184348 089205 856269 309947 810780 801534 176547 723670 724547 612138 401977 280107 943297 242834 720391 635004 772060 821762 885300 307828 511096 142948 > 32¹⁰³ [i]