MinT - Best Known (113−64, 113, s)-Nets in Base 8

Best Known (113−64, 113, s)-Nets in Base 8

(113−64, 113, 98)-Net over F₈ — Constructive and digital

Digital (49, 113, 98)-net over F₈, using

t-expansion [i] based on digital (37, 113, 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]

(113−64, 113, 144)-Net over F₈ — Digital

Digital (49, 113, 144)-net over F₈, using

t-expansion [i] based on digital (45, 113, 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]

(113−64, 113, 2803)-Net in Base 8 — Upper bound on s

There is no (49, 113, 2804)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 124015 876619 542910 666133 173746 501591 951957 930140 187475 714287 358494 016356 122830 297661 921297 611242 128077 > 8¹¹³ [i]