MinT - Best Known (53, 53+114, s)-Nets in Base 8

Best Known (53, 53+114, s)-Nets in Base 8

(53, 53+114, 98)-Net over F₈ — Constructive and digital

Digital (53, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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]

(53, 53+114, 144)-Net over F₈ — Digital

Digital (53, 167, 144)-net over F₈, using

t-expansion [i] based on digital (45, 167, 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]

(53, 53+114, 1359)-Net in Base 8 — Upper bound on s

There is no (53, 167, 1360)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6 589793 523145 398761 013146 122683 616770 467751 756341 813459 799364 758692 482207 792246 821670 991121 173110 149059 172457 463876 624857 728679 165286 467471 987024 428860 > 8¹⁶⁷ [i]