MinT - Best Known (161−99, 161, s)-Nets in Base 8

Best Known (161−99, 161, s)-Nets in Base 8

(161−99, 161, 98)-Net over F₈ — Constructive and digital

Digital (62, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(161−99, 161, 144)-Net over F₈ — Digital

Digital (62, 161, 144)-net over F₈, using

t-expansion [i] based on digital (45, 161, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(161−99, 161, 2396)-Net in Base 8 — Upper bound on s

There is no (62, 161, 2397)-net in base 8, because

1 times m-reduction [i] would yield (62, 160, 2397)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 175675 193650 592454 485846 661883 564638 931408 449285 468675 623805 619072 260626 748609 831680 377472 604515 883161 608686 342935 093867 371604 907917 008581 547176 > 8¹⁶⁰ [i]