MinT - Best Known (164−114, 164, s)-Nets in Base 8

Best Known (164−114, 164, s)-Nets in Base 8

(164−114, 164, 98)-Net over F₈ — Constructive and digital

Digital (50, 164, 98)-net over F₈, using

t-expansion [i] based on digital (37, 164, 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]

(164−114, 164, 144)-Net over F₈ — Digital

Digital (50, 164, 144)-net over F₈, using

t-expansion [i] based on digital (45, 164, 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]

(164−114, 164, 1215)-Net in Base 8 — Upper bound on s

There is no (50, 164, 1216)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13272 055041 804082 136583 044158 438201 389429 414168 329749 938901 587675 026899 126741 816591 705064 992838 599445 482165 614246 372268 793319 807141 896002 659875 585387 > 8¹⁶⁴ [i]