MinT - Best Known (75−42, 75, s)-Nets in Base 32

Best Known (75−42, 75, s)-Nets in Base 32

(75−42, 75, 174)-Net over F₃₂ — Constructive and digital

Digital (33, 75, 174)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 26, 76)-net over F₃₂, using
  - net from sequence [i] based on digital (5, 75)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 5 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]
2. digital (7, 49, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 7 and N(F) ≥ 98, using
      - a function field by SÃ©mirat [i]

(75−42, 75, 288)-Net in Base 32 — Constructive

(33, 75, 288)-net in base 32, using

9 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
- base change [i] based on digital (9, 60, 288)-net over F₁₂₈, using
  - net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
      - a function field by SÃ©mirat [i]

(75−42, 75, 294)-Net over F₃₂ — Digital

Digital (33, 75, 294)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(75−42, 75, 342)-Net in Base 32

(33, 75, 342)-net in base 32, using

3 times m-reduction [i] based on (33, 78, 342)-net in base 32, using
- base change [i] based on digital (20, 65, 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]

(75−42, 75, 66465)-Net in Base 32 — Upper bound on s

There is no (33, 75, 66466)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 76967 433841 295634 619421 686951 978810 558419 925462 010768 287808 808787 124012 236120 731008 220523 446120 380399 544915 030584 > 32⁷⁵ [i]