MinT - Best Known (88−67, 88, s)-Nets in Base 32

Best Known (88−67, 88, s)-Nets in Base 32

(88−67, 88, 120)-Net over F₃₂ — Constructive and digital

Digital (21, 88, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 88, 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]

(88−67, 88, 128)-Net in Base 32 — Constructive

(21, 88, 128)-net in base 32, using

8 times m-reduction [i] based on (21, 96, 128)-net in base 32, using
- base change [i] based on digital (5, 80, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(88−67, 88, 185)-Net over F₃₂ — Digital

Digital (21, 88, 185)-net over F₃₂, using

net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
  - a curve from the manYPoints database [i]

(88−67, 88, 3928)-Net in Base 32 — Upper bound on s

There is no (21, 88, 3929)-net in base 32, because

1 times m-reduction [i] would yield (21, 87, 3929)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 89045 163656 184717 018097 510413 492291 399446 174335 733068 916331 631619 726895 199078 767819 402847 134274 028051 081894 927053 079658 375968 595024 > 32⁸⁷ [i]