MinT - Best Known (173−112, 173, s)-Nets in Base 8

Best Known (173−112, 173, s)-Nets in Base 8

(173−112, 173, 98)-Net over F₈ — Constructive and digital

Digital (61, 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]

(173−112, 173, 144)-Net over F₈ — Digital

Digital (61, 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]

(173−112, 173, 1876)-Net in Base 8 — Upper bound on s

There is no (61, 173, 1877)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 740930 822704 108905 491151 885815 833705 572220 260710 630237 658477 809991 200431 152836 158602 906402 402978 640523 201716 403920 057536 061272 269340 276357 676728 359743 247800 > 8¹⁷³ [i]