MinT - Best Known (106−77, 106, s)-Nets in Base 32

Best Known (106−77, 106, s)-Nets in Base 32

(106−77, 106, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 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]

(106−77, 106, 177)-Net in Base 32 — Constructive

(29, 106, 177)-net in base 32, using

t-expansion [i] based on (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]

(106−77, 106, 257)-Net over F₃₂ — Digital

Digital (29, 106, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 106, 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]

(106−77, 106, 6969)-Net in Base 32 — Upper bound on s

There is no (29, 106, 6970)-net in base 32, because

1 times m-reduction [i] would yield (29, 105, 6970)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 110 326793 393627 870521 180238 823452 393425 370913 150349 101875 404387 390438 380145 791018 728188 259949 463752 500100 421958 622914 450753 719797 327949 394733 286880 640127 591300 > 32¹⁰⁵ [i]