MinT - Best Known (52, 155, s)-Nets in Base 8

Best Known (52, 155, s)-Nets in Base 8

(52, 155, 98)-Net over F₈ — Constructive and digital

Digital (52, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 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]

(52, 155, 144)-Net over F₈ — Digital

Digital (52, 155, 144)-net over F₈, using

t-expansion [i] based on digital (45, 155, 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]

(52, 155, 1480)-Net in Base 8 — Upper bound on s

There is no (52, 155, 1481)-net in base 8, because

1 times m-reduction [i] would yield (52, 154, 1481)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 086156 232849 691877 951311 137245 068240 631462 624107 898187 470308 375607 328687 014217 109957 326720 990184 796150 361507 592323 350148 577636 174779 810208 > 8¹⁵⁴ [i]