MinT - Best Known (36, 173, s)-Nets in Base 8

Best Known (36, 173, s)-Nets in Base 8

(36, 173, 65)-Net over F₈ — Constructive and digital

Digital (36, 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]

(36, 173, 112)-Net over F₈ — Digital

Digital (36, 173, 112)-net over F₈, using

t-expansion [i] based on digital (35, 173, 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]

(36, 173, 676)-Net in Base 8 — Upper bound on s

There is no (36, 173, 677)-net in base 8, because

1 times m-reduction [i] would yield (36, 172, 677)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 222948 621888 800561 642332 370754 771727 501618 675757 162508 230458 052643 137450 312153 420222 786640 436576 353000 111814 990300 621761 995326 416829 350795 566951 253930 390154 > 8¹⁷² [i]