MinT - Best Known (66, 66+97, s)-Nets in Base 8

Best Known (66, 66+97, s)-Nets in Base 8

(66, 66+97, 98)-Net over F₈ — Constructive and digital

Digital (66, 163, 98)-net over F₈, using

t-expansion [i] based on digital (37, 163, 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]

(66, 66+97, 144)-Net over F₈ — Digital

Digital (66, 163, 144)-net over F₈, using

t-expansion [i] based on digital (45, 163, 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]

(66, 66+97, 2959)-Net in Base 8 — Upper bound on s

There is no (66, 163, 2960)-net in base 8, because

1 times m-reduction [i] would yield (66, 162, 2960)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 201 768683 977923 213666 036873 832512 311593 339631 404574 102089 852479 414309 678152 689400 007095 654739 894760 348608 956307 442078 949726 960248 951080 179283 498408 > 8¹⁶² [i]