MinT - Best Known (43, 43+49, s)-Nets in Base 32

Best Known (43, 43+49, s)-Nets in Base 32

(43, 43+49, 218)-Net over F₃₂ — Constructive and digital

Digital (43, 92, 218)-net over F₃₂, using

1 times m-reduction [i] based on digital (43, 93, 218)-net over F₃₂, using
- (u,Â u+v)-construction [i] based on
  1. digital (7, 32, 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, 61, 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]

(43, 43+49, 288)-Net in Base 32 — Constructive

(43, 92, 288)-net in base 32, using

t-expansion [i] based on (40, 92, 288)-net in base 32, using
- 16 times m-reduction [i] based on (40, 108, 288)-net in base 32, using
  - base change [i] based on (22, 90, 288)-net in base 64, using
    - 1 times m-reduction [i] based on (22, 91, 288)-net in base 64, using
      - base change [i] based on digital (9, 78, 288)-net over F₁₂₈, using
        net from sequence [i] based on digital (9, 287)-sequence over F₁₂₈, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 9 and N(F) ≥ 288, using
        a function field by SÃ©mirat [i]

(43, 43+49, 466)-Net over F₃₂ — Digital

Digital (43, 92, 466)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+49, 161062)-Net in Base 32 — Upper bound on s

There is no (43, 92, 161063)-net in base 32, because

1 times m-reduction [i] would yield (43, 91, 161063)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 93039 650833 804298 993183 590416 017698 395127 944618 364597 715139 738084 206656 822556 391767 802377 327419 262658 405283 227271 705631 346873 454602 336916 > 32⁹¹ [i]