MinT - Best Known (60, 60+107, s)-Nets in Base 8

Best Known (60, 60+107, s)-Nets in Base 8

(60, 60+107, 98)-Net over F₈ — Constructive and digital

Digital (60, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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]

(60, 60+107, 144)-Net over F₈ — Digital

Digital (60, 167, 144)-net over F₈, using

t-expansion [i] based on digital (45, 167, 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]

(60, 60+107, 1949)-Net in Base 8 — Upper bound on s

There is no (60, 167, 1950)-net in base 8, because

1 times m-reduction [i] would yield (60, 166, 1950)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 835643 432516 304779 148931 239426 712045 341556 619690 165488 120723 747304 505542 263194 393624 983556 537976 217740 740425 592539 880067 851323 625668 686928 064548 912212 > 8¹⁶⁶ [i]