MinT - Best Known (97−67, 97, s)-Nets in Base 8

Best Known (97−67, 97, s)-Nets in Base 8

(97−67, 97, 65)-Net over F₈ — Constructive and digital

Digital (30, 97, 65)-net over F₈, using

t-expansion [i] based on digital (14, 97, 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]

(97−67, 97, 97)-Net over F₈ — Digital

Digital (30, 97, 97)-net over F₈, using

t-expansion [i] based on digital (28, 97, 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]

(97−67, 97, 776)-Net in Base 8 — Upper bound on s

There is no (30, 97, 777)-net in base 8, because

1 times m-reduction [i] would yield (30, 96, 777)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 510 012810 889212 800363 913563 516076 902003 982155 280538 725449 157677 051910 604986 701281 155840 > 8⁹⁶ [i]