MinT - Best Known (106−46, 106, s)-Nets in Base 32

Best Known (106−46, 106, s)-Nets in Base 32

(106−46, 106, 294)-Net over F₃₂ — Constructive and digital

Digital (60, 106, 294)-net over F₃₂, using

t-expansion [i] based on digital (59, 106, 294)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 22, 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, 30, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (7, 54, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(106−46, 106, 513)-Net in Base 32 — Constructive

(60, 106, 513)-net in base 32, using

t-expansion [i] based on (46, 106, 513)-net in base 32, using
- 2 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
  - base change [i] based on digital (28, 90, 513)-net over F₆₄, using
    - net from sequence [i] based on digital (28, 512)-sequence over F₆₄, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 28 and N(F) ≥ 513, using
        the Hermitian function field over F₆₄ [i]

(106−46, 106, 2019)-Net over F₃₂ — Digital

Digital (60, 106, 2019)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(106−46, 106, 2629485)-Net in Base 32 — Upper bound on s

There is no (60, 106, 2629486)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3514 786748 419119 218184 897003 750182 376412 233530 500332 545734 849466 538549 758746 841209 638960 352753 084503 323869 812997 150787 230472 907750 719331 978464 318954 958766 591672 > 32¹⁰⁶ [i]