MinT - Best Known (29, 78, s)-Nets in Base 32

Best Known (29, 78, s)-Nets in Base 32

(29, 78, 120)-Net over F₃₂ — Constructive and digital

Digital (29, 78, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 78, 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]

(29, 78, 216)-Net in Base 32 — Constructive

(29, 78, 216)-net in base 32, using

6 times m-reduction [i] based on (29, 84, 216)-net in base 32, using
- base change [i] based on digital (5, 60, 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]

(29, 78, 257)-Net over F₃₂ — Digital

Digital (29, 78, 257)-net over F₃₂, using

t-expansion [i] based on digital (28, 78, 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]

(29, 78, 267)-Net in Base 32

(29, 78, 267)-net in base 32, using

base change [i] based on digital (16, 65, 267)-net over F₆₄, using
- net from sequence [i] based on digital (16, 266)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 16 and N(F) ≥ 267, using
    - a curve from the manYPoints database [i]

(29, 78, 21319)-Net in Base 32 — Upper bound on s

There is no (29, 78, 21320)-net in base 32, because

1 times m-reduction [i] would yield (29, 77, 21320)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 78 861674 847765 732233 174212 328684 024310 932614 764334 303894 080136 885195 322241 641797 986072 319264 894926 373806 311663 902712 > 32⁷⁷ [i]