MinT - Best Known (172−124, 172, s)-Nets in Base 8

Best Known (172−124, 172, s)-Nets in Base 8

(172−124, 172, 98)-Net over F₈ — Constructive and digital

Digital (48, 172, 98)-net over F₈, using

t-expansion [i] based on digital (37, 172, 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]

(172−124, 172, 144)-Net over F₈ — Digital

Digital (48, 172, 144)-net over F₈, using

t-expansion [i] based on digital (45, 172, 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]

(172−124, 172, 1055)-Net in Base 8 — Upper bound on s

There is no (48, 172, 1056)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 218911 051923 230348 619289 453524 304056 188290 443632 562203 842735 135563 985874 471716 538021 738992 371402 995207 929371 053576 060638 758720 708581 233630 906917 404841 379168 > 8¹⁷² [i]