MinT - Best Known (70−48, 70, s)-Nets in Base 32

Best Known (70−48, 70, s)-Nets in Base 32

(70−48, 70, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 70, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 70, 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]

(70−48, 70, 177)-Net in Base 32 — Constructive

(22, 70, 177)-net in base 32, using

20 times m-reduction [i] based on (22, 90, 177)-net in base 32, using
- base change [i] based on digital (7, 75, 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]

(70−48, 70, 185)-Net over F₃₂ — Digital

Digital (22, 70, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 70, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(70−48, 70, 225)-Net in Base 32

(22, 70, 225)-net in base 32, using

2 times m-reduction [i] based on (22, 72, 225)-net in base 32, using
- base change [i] based on digital (10, 60, 225)-net over F₆₄, using
  - net from sequence [i] based on digital (10, 224)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 10 and N(F) ≥ 225, using
      - a curve from the manYPoints database [i]

(70−48, 70, 7750)-Net in Base 32 — Upper bound on s

There is no (22, 70, 7751)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2296 399589 848883 681306 103670 221152 347180 526876 235228 508631 231383 694950 722476 510227 914830 043900 569739 017176 > 32⁷⁰ [i]