MinT - Best Known (110−75, 110, s)-Nets in Base 32

Best Known (110−75, 110, s)-Nets in Base 32

(110−75, 110, 120)-Net over F₃₂ — Constructive and digital

Digital (35, 110, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 110, 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]

(110−75, 110, 177)-Net in Base 32 — Constructive

(35, 110, 177)-net in base 32, using

32² times duplication [i] based on (33, 108, 177)-net in base 32, using
- t-expansion [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]

(110−75, 110, 273)-Net over F₃₂ — Digital

Digital (35, 110, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 110, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(110−75, 110, 12823)-Net in Base 32 — Upper bound on s

There is no (35, 110, 12824)-net in base 32, because

1 times m-reduction [i] would yield (35, 109, 12824)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 115 488862 524400 653772 158115 983215 493105 784036 446091 944176 587428 245062 669317 698456 834116 438884 681442 703544 287499 871692 732284 226049 237560 930878 351690 636910 908556 152496 > 32¹⁰⁹ [i]