MinT - Best Known (24, 107, s)-Nets in Base 32

Best Known (24, 107, s)-Nets in Base 32

(24, 107, 120)-Net over F₃₂ — Constructive and digital

Digital (24, 107, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 107, 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]

(24, 107, 128)-Net in Base 32 — Constructive

(24, 107, 128)-net in base 32, using

t-expansion [i] based on (23, 107, 128)-net in base 32, using
- 1 times m-reduction [i] based on (23, 108, 128)-net in base 32, using
  - base change [i] based on digital (5, 90, 128)-net over F₆₄, using
    - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
        a function field by SÃ©mirat [i]

(24, 107, 225)-Net over F₃₂ — Digital

Digital (24, 107, 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]

(24, 107, 4032)-Net in Base 32 — Upper bound on s

There is no (24, 107, 4033)-net in base 32, because

1 times m-reduction [i] would yield (24, 106, 4033)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3515 163452 256878 569878 999111 837725 582032 188106 451108 054724 785241 266116 064108 349571 178389 624668 878593 756785 187844 186708 389404 619308 796769 399588 970258 844440 488640 > 32¹⁰⁶ [i]