MinT - Best Known (32, 32+120, s)-Nets in Base 8

Best Known (32, 32+120, s)-Nets in Base 8

(32, 32+120, 65)-Net over F₈ — Constructive and digital

Digital (32, 152, 65)-net over F₈, using

t-expansion [i] based on digital (14, 152, 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, 32+120, 97)-Net over F₈ — Digital

Digital (32, 152, 97)-net over F₈, using

t-expansion [i] based on digital (28, 152, 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, 32+120, 605)-Net in Base 8 — Upper bound on s

There is no (32, 152, 606)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 197152 199735 786444 514178 884439 308137 208780 209546 430549 978439 346470 951678 859487 542557 130770 788003 952448 119356 822536 254439 158317 984456 318866 > 8¹⁵² [i]