MinT - Best Known (32, 32+65, s)-Nets in Base 32

Best Known (32, 32+65, s)-Nets in Base 32

(32, 32+65, 120)-Net over F₃₂ — Constructive and digital

Digital (32, 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]

(32, 32+65, 192)-Net in Base 32 — Constructive

(32, 97, 192)-net in base 32, using

t-expansion [i] based on (31, 97, 192)-net in base 32, using
- 1 times m-reduction [i] based on (31, 98, 192)-net in base 32, using
  - base change [i] based on digital (3, 70, 192)-net over F₁₂₈, using
    - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
        a function field by SÃ©mirat [i]

(32, 32+65, 273)-Net over F₃₂ — Digital

Digital (32, 97, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 97, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(32, 32+65, 13503)-Net in Base 32 — Upper bound on s

There is no (32, 97, 13504)-net in base 32, because

1 times m-reduction [i] would yield (32, 96, 13504)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 127513 533416 297989 935433 781713 282549 106464 579358 522357 135236 448370 818936 975734 074115 325179 991608 183619 203977 831215 606196 465731 719810 559992 267191 > 32⁹⁶ [i]