MinT - Best Known (35, 35+135, s)-Nets in Base 8

Best Known (35, 35+135, s)-Nets in Base 8

(35, 35+135, 65)-Net over F₈ — Constructive and digital

Digital (35, 170, 65)-net over F₈, using

t-expansion [i] based on digital (14, 170, 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]

(35, 35+135, 112)-Net over F₈ — Digital

Digital (35, 170, 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]

(35, 35+135, 656)-Net in Base 8 — Upper bound on s

There is no (35, 170, 657)-net in base 8, because

1 times m-reduction [i] would yield (35, 169, 657)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 428 101114 055141 504833 219638 108522 186406 759976 753931 066850 416546 153522 977904 554788 557686 504898 334183 338952 267665 559540 429211 881744 331411 621577 018268 211936 > 8¹⁶⁹ [i]