MinT - Best Known (142−95, 142, s)-Nets in Base 8

Best Known (142−95, 142, s)-Nets in Base 8

(142−95, 142, 98)-Net over F₈ — Constructive and digital

Digital (47, 142, 98)-net over F₈, using

t-expansion [i] based on digital (37, 142, 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]

(142−95, 142, 144)-Net over F₈ — Digital

Digital (47, 142, 144)-net over F₈, using

t-expansion [i] based on digital (45, 142, 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]

(142−95, 142, 1314)-Net in Base 8 — Upper bound on s

There is no (47, 142, 1315)-net in base 8, because

1 times m-reduction [i] would yield (47, 141, 1315)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 22 363914 287709 133655 351613 842729 186114 637345 189068 908981 822718 496710 152206 640446 733681 147525 589409 296436 031713 881673 689417 147648 > 8¹⁴¹ [i]