MinT - Best Known (171−135, 171, s)-Nets in Base 8

Best Known (171−135, 171, s)-Nets in Base 8

(171−135, 171, 65)-Net over F₈ — Constructive and digital

Digital (36, 171, 65)-net over F₈, using

t-expansion [i] based on digital (14, 171, 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]

(171−135, 171, 112)-Net over F₈ — Digital

Digital (36, 171, 112)-net over F₈, using

t-expansion [i] based on digital (35, 171, 112)-net over F₈, using
- net from sequence [i] based on digital (35, 111)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
    - a curve from the manYPoints database [i]

(171−135, 171, 678)-Net in Base 8 — Upper bound on s

There is no (36, 171, 679)-net in base 8, because

1 times m-reduction [i] would yield (36, 170, 679)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3422 982464 834463 450517 137864 702678 721973 481965 792802 293780 546972 243493 994937 676557 933336 931580 829898 475973 364375 430345 130663 506167 839494 645004 748817 711368 > 8¹⁷⁰ [i]