MinT - Best Known (44, 94, s)-Nets in Base 32

Best Known (44, 94, s)-Nets in Base 32

(44, 94, 218)-Net over F₃₂ — Constructive and digital

Digital (44, 94, 218)-net over F₃₂, using

2 times m-reduction [i] based on digital (44, 96, 218)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 33, 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 (11, 63, 120)-net over F₃₂, using
    - net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
        a function field by SÃ©mirat [i]

(44, 94, 478)-Net over F₃₂ — Digital

Digital (44, 94, 478)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 94, 513)-Net in Base 32 — Constructive

(44, 94, 513)-net in base 32, using

2 times m-reduction [i] based on (44, 96, 513)-net in base 32, using
- base change [i] based on digital (28, 80, 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]

(44, 94, 149827)-Net in Base 32 — Upper bound on s

There is no (44, 94, 149828)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3048 942217 790872 412171 115491 034659 933546 471700 315631 642860 245609 523768 878738 005611 206363 402608 647807 065306 987037 955412 790420 355714 436414 505000 > 32⁹⁴ [i]