MinT - Best Known (49, 166, s)-Nets in Base 8

Best Known (49, 166, s)-Nets in Base 8

(49, 166, 98)-Net over F₈ — Constructive and digital

Digital (49, 166, 98)-net over F₈, using

t-expansion [i] based on digital (37, 166, 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]

(49, 166, 144)-Net over F₈ — Digital

Digital (49, 166, 144)-net over F₈, using

t-expansion [i] based on digital (45, 166, 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]

(49, 166, 1152)-Net in Base 8 — Upper bound on s

There is no (49, 166, 1153)-net in base 8, because

1 times m-reduction [i] would yield (49, 165, 1153)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 103394 590739 815437 067301 652224 492919 303589 028138 686581 688078 822192 290384 795511 981983 804665 709225 921274 509938 433967 690350 057411 668846 837103 762565 586368 > 8¹⁶⁵ [i]