MinT - Best Known (101−58, 101, s)-Nets in Base 32

Best Known (101−58, 101, s)-Nets in Base 32

(101−58, 101, 196)-Net over F₃₂ — Constructive and digital

Digital (43, 101, 196)-net over F₃₂, using

(u,Â u+v)-construction [i] based on
1. digital (7, 36, 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]
2. digital (7, 65, 98)-net over F₃₂, using
  - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(101−58, 101, 288)-Net in Base 32 — Constructive

(43, 101, 288)-net in base 32, using

t-expansion [i] based on (40, 101, 288)-net in base 32, using
- 7 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]

(101−58, 101, 320)-Net over F₃₂ — Digital

Digital (43, 101, 320)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−58, 101, 425)-Net in Base 32

(43, 101, 425)-net in base 32, using

1 times m-reduction [i] based on (43, 102, 425)-net in base 32, using
- base change [i] based on digital (26, 85, 425)-net over F₆₄, using
  - net from sequence [i] based on digital (26, 424)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 26 and N(F) ≥ 425, using
      - a curve from the manYPoints database [i]

(101−58, 101, 65725)-Net in Base 32 — Upper bound on s

There is no (43, 101, 65726)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 104 758837 863167 323521 165459 193887 783842 978473 931783 232502 916821 344865 942710 736626 139668 328244 044242 386493 639954 222701 760761 668961 820495 748445 819201 337861 > 32¹⁰¹ [i]