MinT - Best Known (148−99, 148, s)-Nets in Base 8

Best Known (148−99, 148, s)-Nets in Base 8

(148−99, 148, 98)-Net over F₈ — Constructive and digital

Digital (49, 148, 98)-net over F₈, using

t-expansion [i] based on digital (37, 148, 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]

(148−99, 148, 144)-Net over F₈ — Digital

Digital (49, 148, 144)-net over F₈, using

t-expansion [i] based on digital (45, 148, 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]

(148−99, 148, 1367)-Net in Base 8 — Upper bound on s

There is no (49, 148, 1368)-net in base 8, because

1 times m-reduction [i] would yield (49, 147, 1368)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 856268 745281 269453 558631 169607 580315 018623 004129 092703 941440 684771 052671 153346 576503 405632 392737 686116 315987 432220 770242 617459 439042 > 8¹⁴⁷ [i]