MinT - Best Known (39, 39+69, s)-Nets in Base 32

Best Known (39, 39+69, s)-Nets in Base 32

(39, 39+69, 120)-Net over F₃₂ — Constructive and digital

Digital (39, 108, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 108, 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]

(39, 39+69, 216)-Net in Base 32 — Constructive

(39, 108, 216)-net in base 32, using

t-expansion [i] based on (36, 108, 216)-net in base 32, using
- base change [i] based on (18, 90, 216)-net in base 64, using
  - 1 times m-reduction [i] based on (18, 91, 216)-net in base 64, using
    - base change [i] based on digital (5, 78, 216)-net over F₁₂₈, using
      - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
        a function field by SÃ©mirat [i]

(39, 39+69, 291)-Net over F₃₂ — Digital

Digital (39, 108, 291)-net over F₃₂, using

t-expansion [i] based on digital (38, 108, 291)-net over F₃₂, using
- net from sequence [i] based on digital (38, 290)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 38 and N(F) ≥ 291, using
    - a curve from the manYPoints database [i]

(39, 39+69, 342)-Net in Base 32

(39, 108, 342)-net in base 32, using

t-expansion [i] based on (38, 108, 342)-net in base 32, using
- base change [i] based on digital (20, 90, 342)-net over F₆₄, using
  - net from sequence [i] based on digital (20, 341)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 20 and N(F) ≥ 342, using
      - a curve from the manYPoints database [i]

(39, 39+69, 23800)-Net in Base 32 — Upper bound on s

There is no (39, 108, 23801)-net in base 32, because

1 times m-reduction [i] would yield (39, 107, 23801)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 112533 313279 787410 596190 760092 339907 824453 138988 027413 486782 674321 714779 468185 965715 276498 327163 352051 054549 243487 709861 473689 856656 327200 573734 561373 179306 177588 > 32¹⁰⁷ [i]