MinT - Best Known (97−73, 97, s)-Nets in Base 32

Best Known (97−73, 97, s)-Nets in Base 32

(97−73, 97, 120)-Net over F₃₂ — Constructive and digital

Digital (24, 97, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 97, 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]

(97−73, 97, 177)-Net in Base 32 — Constructive

(24, 97, 177)-net in base 32, using

5 times m-reduction [i] based on (24, 102, 177)-net in base 32, using
- base change [i] based on digital (7, 85, 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]

(97−73, 97, 225)-Net over F₃₂ — Digital

Digital (24, 97, 225)-net over F₃₂, using

net from sequence [i] based on digital (24, 224)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
  - a curve from the manYPoints database [i]

(97−73, 97, 4735)-Net in Base 32 — Upper bound on s

There is no (24, 97, 4736)-net in base 32, because

1 times m-reduction [i] would yield (24, 96, 4736)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 124201 793725 021860 995665 469283 919655 057987 154882 633249 078788 092352 712320 964394 840029 659189 918372 344180 119354 861602 754768 608676 846347 842819 744581 > 32⁹⁶ [i]