MinT - Best Known (95−40, 95, s)-Nets in Base 32

Best Known (95−40, 95, s)-Nets in Base 32

(95−40, 95, 294)-Net over F₃₂ — Constructive and digital

Digital (55, 95, 294)-net over F₃₂, using

t-expansion [i] based on digital (54, 95, 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, 27, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)
  3. digital (7, 48, 98)-net over F₃₂, using
    - net from sequence [i] based on digital (7, 97)-sequence over F₃₂ (see above)

(95−40, 95, 513)-Net in Base 32 — Constructive

(55, 95, 513)-net in base 32, using

t-expansion [i] based on (46, 95, 513)-net in base 32, using
- 13 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]

(95−40, 95, 2323)-Net over F₃₂ — Digital

Digital (55, 95, 2323)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−40, 95, 3779251)-Net in Base 32 — Upper bound on s

There is no (55, 95, 3779252)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 97555 016800 533993 079435 306240 403866 600861 178777 039716 216725 117672 759793 420207 080309 233337 131206 192681 945685 239640 223439 501892 973991 539455 383736 > 32⁹⁵ [i]