MinT - Best Known (99−59, 99, s)-Nets in Base 32

Best Known (99−59, 99, s)-Nets in Base 32

(99−59, 99, 162)-Net over F₃₂ — Constructive and digital

Digital (40, 99, 162)-net over F₃₂, using

1 times m-reduction [i] based on digital (40, 100, 162)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (3, 33, 64)-net over F₃₂, using
    - net from sequence [i] based on digital (3, 63)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 3 and N(F) ≥ 64, using
        a function field by SÃ©mirat [i]
  2. digital (7, 67, 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]

(99−59, 99, 288)-Net in Base 32 — Constructive

(40, 99, 288)-net in base 32, using

9 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
- base change [i] based on (22, 90, 288)-net in base 64, using
  - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
    - base change [i] based on digital (9, 78, 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]

(99−59, 99, 293)-Net over F₃₂ — Digital

Digital (40, 99, 293)-net over F₃₂, using

net from sequence [i] based on digital (40, 292)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 40 and N(F) ≥ 293, using
  - a curve from the manYPoints database [i]

(99−59, 99, 342)-Net in Base 32

(40, 99, 342)-net in base 32, using

t-expansion [i] based on (38, 99, 342)-net in base 32, using
- 9 times m-reduction [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]

(99−59, 99, 45918)-Net in Base 32 — Upper bound on s

There is no (40, 99, 45919)-net in base 32, because

1 times m-reduction [i] would yield (40, 98, 45919)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3197 614007 302113 114328 620199 103205 261759 627428 868983 951493 861524 940417 800706 729314 377723 055806 070607 689265 281970 220400 446795 509005 573474 639122 538026 > 32⁹⁸ [i]