MinT - Best Known (133−88, 133, s)-Nets in Base 8

Best Known (133−88, 133, s)-Nets in Base 8

(133−88, 133, 98)-Net over F₈ — Constructive and digital

Digital (45, 133, 98)-net over F₈, using

t-expansion [i] based on digital (37, 133, 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]

(133−88, 133, 144)-Net over F₈ — Digital

Digital (45, 133, 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]

(133−88, 133, 1295)-Net in Base 8 — Upper bound on s

There is no (45, 133, 1296)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 309638 433133 554528 242887 931914 927051 677837 346711 089975 806714 584717 389904 875751 544306 238746 113846 654947 254884 466100 987720 > 8¹³³ [i]