MinT - Best Known (32, 173, s)-Nets in Base 8

Best Known (32, 173, s)-Nets in Base 8

(32, 173, 65)-Net over F₈ — Constructive and digital

Digital (32, 173, 65)-net over F₈, using

t-expansion [i] based on digital (14, 173, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(32, 173, 97)-Net over F₈ — Digital

Digital (32, 173, 97)-net over F₈, using

t-expansion [i] based on digital (28, 173, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(32, 173, 592)-Net in Base 8 — Upper bound on s

There is no (32, 173, 593)-net in base 8, because

1 times m-reduction [i] would yield (32, 172, 593)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 223092 284719 343243 958905 298622 823681 649512 972331 714888 833035 538206 291838 804603 349919 402446 773873 673022 041668 144868 787202 883298 996100 681417 780568 767206 631016 > 8¹⁷² [i]