MinT - Best Known (61, 170, s)-Nets in Base 8

Best Known (61, 170, s)-Nets in Base 8

(61, 170, 98)-Net over F₈ — Constructive and digital

Digital (61, 170, 98)-net over F₈, using

t-expansion [i] based on digital (37, 170, 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]

(61, 170, 144)-Net over F₈ — Digital

Digital (61, 170, 144)-net over F₈, using

t-expansion [i] based on digital (45, 170, 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]

(61, 170, 1974)-Net in Base 8 — Upper bound on s

There is no (61, 170, 1975)-net in base 8, because

1 times m-reduction [i] would yield (61, 169, 1975)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 429 878534 399770 715675 866437 911811 909979 248397 928147 513595 864740 470038 400374 875969 670493 254803 501714 230738 083223 990053 577421 263982 863182 320900 532715 488797 > 8¹⁶⁹ [i]