MinT - Best Known (45, 169, s)-Nets in Base 8

Best Known (45, 169, s)-Nets in Base 8

(45, 169, 98)-Net over F₈ — Constructive and digital

Digital (45, 169, 98)-net over F₈, using

t-expansion [i] based on digital (37, 169, 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]

(45, 169, 144)-Net over F₈ — Digital

Digital (45, 169, 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]

(45, 169, 950)-Net in Base 8 — Upper bound on s

There is no (45, 169, 951)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 421 316082 318314 299802 862089 212338 283010 808309 330402 198096 851535 493355 745827 795465 727056 297957 780650 122872 350182 207354 362830 466146 047238 974441 387745 984592 > 8¹⁶⁹ [i]