MinT - Best Known (99−58, 99, s)-Nets in Base 32

Best Known (99−58, 99, s)-Nets in Base 32

(99−58, 99, 174)-Net over F₃₂ — Constructive and digital

Digital (41, 99, 174)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (5, 34, 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, 65, 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]

(99−58, 99, 288)-Net in Base 32 — Constructive

(41, 99, 288)-net in base 32, using

t-expansion [i] based on (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]

(99−58, 99, 308)-Net over F₃₂ — Digital

Digital (41, 99, 308)-net over F₃₂, using

net from sequence [i] based on digital (41, 307)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 41 and N(F) ≥ 308, using
  - a curve from the manYPoints database [i]

(99−58, 99, 342)-Net in Base 32

(41, 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]

(99−58, 99, 51749)-Net in Base 32 — Upper bound on s

There is no (41, 99, 51750)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 102325 696182 854270 557607 363674 222510 000323 577337 649184 427319 670342 268466 832540 620795 197105 293365 633551 636886 045668 252693 139133 861103 795496 178277 889196 > 32⁹⁹ [i]