MinT - Best Known (67, 164, s)-Nets in Base 8

Best Known (67, 164, s)-Nets in Base 8

(67, 164, 98)-Net over F₈ — Constructive and digital

Digital (67, 164, 98)-net over F₈, using

t-expansion [i] based on digital (37, 164, 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]

(67, 164, 144)-Net over F₈ — Digital

Digital (67, 164, 144)-net over F₈, using

t-expansion [i] based on digital (45, 164, 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]

(67, 164, 150)-Net in Base 8

(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]

(67, 164, 3091)-Net in Base 8 — Upper bound on s

There is no (67, 164, 3092)-net in base 8, because

1 times m-reduction [i] would yield (67, 163, 3092)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1604 590832 114966 571532 761086 954083 122898 585472 159825 280964 236457 558892 328412 586809 869652 905037 436128 348201 651742 723952 238169 237355 934752 329427 254112 > 8¹⁶³ [i]