MinT - Best Known (69−49, 69, s)-Nets in Base 32

Best Known (69−49, 69, s)-Nets in Base 32

(69−49, 69, 120)-Net over F₃₂ — Constructive and digital

Digital (20, 69, 120)-net over F₃₂, using

t-expansion [i] based on 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]

(69−49, 69, 177)-Net in Base 32 — Constructive

(20, 69, 177)-net in base 32, using

9 times m-reduction [i] based on (20, 78, 177)-net in base 32, using
- base change [i] based on digital (7, 65, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(69−49, 69, 177)-Net over F₃₂ — Digital

Digital (20, 69, 177)-net over F₃₂, using

net from sequence [i] based on digital (20, 176)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 20 and N(F) ≥ 177, using
  - a curve from the manYPoints database [i]

(69−49, 69, 5803)-Net in Base 32 — Upper bound on s

There is no (20, 69, 5804)-net in base 32, because

1 times m-reduction [i] would yield (20, 68, 5804)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 246165 235962 774039 407190 476040 910475 897585 729716 538411 415998 000634 060019 941938 172244 313130 792351 007922 > 32⁶⁸ [i]