MinT - Best Known (62, 62+109, s)-Nets in Base 8

Best Known (62, 62+109, s)-Nets in Base 8

(62, 62+109, 98)-Net over F₈ — Constructive and digital

Digital (62, 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]

(62, 62+109, 144)-Net over F₈ — Digital

Digital (62, 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]

(62, 62+109, 2052)-Net in Base 8 — Upper bound on s

There is no (62, 171, 2053)-net in base 8, because

1 times m-reduction [i] would yield (62, 170, 2053)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3362 774040 330029 935762 146841 272781 855463 100245 195619 661410 483400 980494 198032 817001 252731 531802 655682 729716 770163 667401 888063 019306 537676 761674 371446 371328 > 8¹⁷⁰ [i]