MinT - Best Known (54, 54+119, s)-Nets in Base 8

Best Known (54, 54+119, s)-Nets in Base 8

(54, 54+119, 98)-Net over F₈ — Constructive and digital

Digital (54, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 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]

(54, 54+119, 144)-Net over F₈ — Digital

Digital (54, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 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]

(54, 54+119, 1362)-Net in Base 8 — Upper bound on s

There is no (54, 173, 1363)-net in base 8, because

1 times m-reduction [i] would yield (54, 172, 1363)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 220127 257918 345292 245605 849956 711712 916604 022211 683245 041796 797202 984640 900881 085226 797615 443193 293432 074286 378509 352547 657805 876802 259253 823360 879078 763648 > 8¹⁷² [i]