MinT - Best Known (129−73, 129, s)-Nets in Base 8

Best Known (129−73, 129, s)-Nets in Base 8

(129−73, 129, 98)-Net over F₈ — Constructive and digital

Digital (56, 129, 98)-net over F₈, using

t-expansion [i] based on digital (37, 129, 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]

(129−73, 129, 144)-Net over F₈ — Digital

Digital (56, 129, 144)-net over F₈, using

t-expansion [i] based on digital (45, 129, 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]

(129−73, 129, 3293)-Net in Base 8 — Upper bound on s

There is no (56, 129, 3294)-net in base 8, because

1 times m-reduction [i] would yield (56, 128, 3294)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 39 621009 893557 060370 516200 508776 288355 211163 208404 683338 335465 259659 536556 410461 510395 766223 973858 707435 559056 841410 > 8¹²⁸ [i]