MinT - Best Known (53, 53+38, s)-Nets in Base 32

Best Known (53, 53+38, s)-Nets in Base 32

(53, 53+38, 294)-Net over F₃₂ — Constructive and digital

Digital (53, 91, 294)-net over F₃₂, using

1 times m-reduction [i] based on digital (53, 92, 294)-net over F₃₂, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (7, 20, 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, 26, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (7, 46, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(53, 53+38, 513)-Net in Base 32 — Constructive

(53, 91, 513)-net in base 32, using

t-expansion [i] based on (46, 91, 513)-net in base 32, using
- 17 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]

(53, 53+38, 2398)-Net over F₃₂ — Digital

Digital (53, 91, 2398)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(53, 53+38, 4137414)-Net in Base 32 — Upper bound on s

There is no (53, 91, 4137415)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93035 638260 121918 602883 793665 846958 252197 644621 632058 363195 472911 670719 923759 133100 384639 274983 213564 429975 630208 397075 650316 455157 372208 > 32⁹¹ [i]