MinT - Best Known (54, 54+100, s)-Nets in Base 8

Best Known (54, 54+100, s)-Nets in Base 8

(54, 54+100, 98)-Net over F₈ — Constructive and digital

Digital (54, 154, 98)-net over F₈, using

t-expansion [i] based on digital (37, 154, 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+100, 144)-Net over F₈ — Digital

Digital (54, 154, 144)-net over F₈, using

t-expansion [i] based on digital (45, 154, 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+100, 1651)-Net in Base 8 — Upper bound on s

There is no (54, 154, 1652)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 078528 969195 255113 336186 819040 120502 889076 444292 595657 676458 957671 232021 965746 885214 046466 594098 904722 508914 294058 801212 858089 112786 758161 > 8¹⁵⁴ [i]