MinT - Best Known (52, 52+42, s)-Nets in Base 32

Best Known (52, 52+42, s)-Nets in Base 32

(52, 52+42, 260)-Net over F₃₂ — Constructive and digital

Digital (52, 94, 260)-net over F₃₂, using

1 times m-reduction [i] based on digital (52, 95, 260)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (3, 17, 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, 28, 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]
  3. digital (7, 50, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(52, 52+42, 513)-Net in Base 32 — Constructive

(52, 94, 513)-net in base 32, using

t-expansion [i] based on (46, 94, 513)-net in base 32, using
- 14 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]

(52, 52+42, 1491)-Net over F₃₂ — Digital

Digital (52, 94, 1491)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(52, 52+42, 1529205)-Net in Base 32 — Upper bound on s

There is no (52, 94, 1529206)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3048 605291 242745 269088 008692 333140 651102 667664 017861 254222 724976 220166 047353 802644 713425 984511 587017 495711 377286 577852 370741 870064 400168 521981 > 32⁹⁴ [i]