MinT - Best Known (35, 109, s)-Nets in Base 32

Best Known (35, 109, s)-Nets in Base 32

(35, 109, 120)-Net over F₃₂ — Constructive and digital

Digital (35, 109, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 109, 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]

(35, 109, 192)-Net in Base 32 — Constructive

(35, 109, 192)-net in base 32, using

32¹ times duplication [i] based on (34, 108, 192)-net in base 32, using
- base change [i] based on (16, 90, 192)-net in base 64, using
  - 1 times m-reduction [i] based on (16, 91, 192)-net in base 64, using
    - base change [i] based on digital (3, 78, 192)-net over F₁₂₈, using
      - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(35, 109, 273)-Net over F₃₂ — Digital

Digital (35, 109, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 109, 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]

(35, 109, 12823)-Net in Base 32 — Upper bound on s

There is no (35, 109, 12824)-net in base 32, because

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]