MinT - Best Known (35, 35+63, s)-Nets in Base 32

Best Known (35, 35+63, s)-Nets in Base 32

(35, 35+63, 120)-Net over F₃₂ — Constructive and digital

Digital (35, 98, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 98, 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, 35+63, 216)-Net in Base 32 — Constructive

(35, 98, 216)-net in base 32, using

7 times m-reduction [i] based on (35, 105, 216)-net in base 32, using
- base change [i] based on digital (5, 75, 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]

(35, 35+63, 273)-Net over F₃₂ — Digital

Digital (35, 98, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 98, 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, 35+63, 281)-Net in Base 32

(35, 98, 281)-net in base 32, using

4 times m-reduction [i] based on (35, 102, 281)-net in base 32, using
- base change [i] based on digital (18, 85, 281)-net over F₆₄, using
  - net from sequence [i] based on digital (18, 280)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 18 and N(F) ≥ 281, using
      - a curve from the manYPoints database [i]

(35, 35+63, 20511)-Net in Base 32 — Upper bound on s

There is no (35, 98, 20512)-net in base 32, because

1 times m-reduction [i] would yield (35, 97, 20512)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 99 984983 131327 955515 128029 490870 826664 191553 725093 278745 771419 268378 175205 981837 524534 435603 346567 857714 328889 848625 903543 840606 524717 290952 441599 > 32⁹⁷ [i]