MinT - Best Known (51, 51+94, s)-Nets in Base 8

Best Known (51, 51+94, s)-Nets in Base 8

(51, 51+94, 98)-Net over F₈ — Constructive and digital

Digital (51, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 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]

(51, 51+94, 144)-Net over F₈ — Digital

Digital (51, 145, 144)-net over F₈, using

t-expansion [i] based on digital (45, 145, 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]

(51, 51+94, 1574)-Net in Base 8 — Upper bound on s

There is no (51, 145, 1575)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 90891 049804 242094 450363 841590 567119 157059 775108 139086 010907 405671 378005 070985 878588 335055 424247 591489 044630 508796 201096 126534 403072 > 8¹⁴⁵ [i]