MinT - Best Known (161−94, 161, s)-Nets in Base 8

Best Known (161−94, 161, s)-Nets in Base 8

(161−94, 161, 98)-Net over F₈ — Constructive and digital

Digital (67, 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]

(161−94, 161, 144)-Net over F₈ — Digital

Digital (67, 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]

(161−94, 161, 150)-Net in Base 8

(67, 161, 150)-net in base 8, using

3 times m-reduction [i] based on (67, 164, 150)-net in base 8, using
- base change [i] based on digital (26, 123, 150)-net over F₁₆, using
  - net from sequence [i] based on digital (26, 149)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 26 and N(F) ≥ 150, using
      - a curve from the manYPoints database [i]

(161−94, 161, 3225)-Net in Base 8 — Upper bound on s

There is no (67, 161, 3226)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 165216 919600 968130 739317 561742 909386 579238 899651 501303 951624 449522 607855 577379 670129 027850 723831 757462 606440 177413 611850 347452 907552 426084 756064 > 8¹⁶¹ [i]