MinT - Best Known (145−96, 145, s)-Nets in Base 8

Best Known (145−96, 145, s)-Nets in Base 8

(145−96, 145, 98)-Net over F₈ — Constructive and digital

Digital (49, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 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]

(145−96, 145, 144)-Net over F₈ — Digital

Digital (49, 145, 144)-net over F₈, using

t-expansion [i] based on digital (45, 145, 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]

(145−96, 145, 1401)-Net in Base 8 — Upper bound on s

There is no (49, 145, 1402)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 90873 840422 938712 757122 025530 746282 743828 530634 379364 630369 310234 197500 461408 468821 463750 439945 346235 644109 897040 187227 453247 692625 > 8¹⁴⁵ [i]