MinT - Best Known (119−67, 119, s)-Nets in Base 8

Best Known (119−67, 119, s)-Nets in Base 8

(119−67, 119, 98)-Net over F₈ — Constructive and digital

Digital (52, 119, 98)-net over F₈, using

t-expansion [i] based on digital (37, 119, 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]

(119−67, 119, 144)-Net over F₈ — Digital

Digital (52, 119, 144)-net over F₈, using

t-expansion [i] based on digital (45, 119, 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]

(119−67, 119, 3167)-Net in Base 8 — Upper bound on s

There is no (52, 119, 3168)-net in base 8, because

1 times m-reduction [i] would yield (52, 118, 3168)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 37040 750406 180523 515391 640540 234631 807912 966935 994959 793722 343682 113494 083109 094029 886983 337819 245260 138730 > 8¹¹⁸ [i]