MinT - Best Known (170−141, 170, s)-Nets in Base 8

Best Known (170−141, 170, s)-Nets in Base 8

(170−141, 170, 65)-Net over F₈ — Constructive and digital

Digital (29, 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]

(170−141, 170, 97)-Net over F₈ — Digital

Digital (29, 170, 97)-net over F₈, using

t-expansion [i] based on digital (28, 170, 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]

(170−141, 170, 538)-Net in Base 8 — Upper bound on s

There is no (29, 170, 539)-net in base 8, because

1 times m-reduction [i] would yield (29, 169, 539)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 446 068517 783683 744960 653949 732492 849936 562899 959994 691262 219201 043561 385595 324958 503800 782877 511923 541478 264758 534749 759489 136660 647681 530611 800480 688144 > 8¹⁶⁹ [i]