MinT - Best Known (66, 66+105, s)-Nets in Base 8

Best Known (66, 66+105, s)-Nets in Base 8

(66, 66+105, 98)-Net over F₈ — Constructive and digital

Digital (66, 171, 98)-net over F₈, using

t-expansion [i] based on digital (37, 171, 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+105, 144)-Net over F₈ — Digital

Digital (66, 171, 144)-net over F₈, using

t-expansion [i] based on digital (45, 171, 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+105, 2556)-Net in Base 8 — Upper bound on s

There is no (66, 171, 2557)-net in base 8, because

1 times m-reduction [i] would yield (66, 170, 2557)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3375 300376 186360 951305 788465 746882 710617 114870 025252 840544 039995 810424 115788 641208 874521 138701 754625 862496 636760 862901 835668 818998 082237 921782 133255 765867 > 8¹⁷⁰ [i]