MinT - Best Known (163−110, 163, s)-Nets in Base 8

Best Known (163−110, 163, s)-Nets in Base 8

(163−110, 163, 98)-Net over F₈ — Constructive and digital

Digital (53, 163, 98)-net over F₈, using

t-expansion [i] based on digital (37, 163, 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]

(163−110, 163, 144)-Net over F₈ — Digital

Digital (53, 163, 144)-net over F₈, using

t-expansion [i] based on digital (45, 163, 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]

(163−110, 163, 1412)-Net in Base 8 — Upper bound on s

There is no (53, 163, 1413)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1631 055563 964174 549857 903890 229400 473013 567035 744285 470990 708341 320446 122586 682461 214040 790944 301080 613782 722522 194391 067302 476471 017867 593195 050112 > 8¹⁶³ [i]