MinT - Best Known (147−111, 147, s)-Nets in Base 8

Best Known (147−111, 147, s)-Nets in Base 8

(147−111, 147, 65)-Net over F₈ — Constructive and digital

Digital (36, 147, 65)-net over F₈, using

t-expansion [i] based on digital (14, 147, 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]

(147−111, 147, 112)-Net over F₈ — Digital

Digital (36, 147, 112)-net over F₈, using

t-expansion [i] based on digital (35, 147, 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]

(147−111, 147, 726)-Net in Base 8 — Upper bound on s

There is no (36, 147, 727)-net in base 8, because

1 times m-reduction [i] would yield (36, 146, 727)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 732597 911463 511339 778607 305647 697116 407385 157817 557560 472391 617259 583957 302112 428978 361782 307357 966003 300387 218429 733411 396390 824848 > 8¹⁴⁶ [i]