MinT - Best Known (105−56, 105, s)-Nets in Base 32

Best Known (105−56, 105, s)-Nets in Base 32

(105−56, 105, 224)-Net over F₃₂ — Constructive and digital

Digital (49, 105, 224)-net over F₃₂, using

2 times m-reduction [i] based on digital (49, 107, 224)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (9, 38, 104)-net over F₃₂, using
    - net from sequence [i] based on digital (9, 103)-sequence over F₃₂, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 9 and N(F) ≥ 104, using
        a function field by SÃ©mirat [i]
  2. digital (11, 69, 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]

(105−56, 105, 513)-Net in Base 32 — Constructive

(49, 105, 513)-net in base 32, using

t-expansion [i] based on (46, 105, 513)-net in base 32, using
- 3 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]

(105−56, 105, 513)-Net over F₃₂ — Digital

Digital (49, 105, 513)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(105−56, 105, 160663)-Net in Base 32 — Upper bound on s

There is no (49, 105, 160664)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 109 849171 341554 822674 156847 870690 336577 801536 040658 992869 833698 069277 917834 759712 180114 420307 547088 860850 028123 329048 567130 894929 296598 087496 060297 479472 638704 > 32¹⁰⁵ [i]