MinT - Best Known (8, 62, s)-Nets in Base 81

Best Known (8, 62, s)-Nets in Base 81

(8, 62, 172)-Net over F₈₁ — Constructive and digital

Digital (8, 62, 172)-net over F₈₁, using

t-expansion [i] based on digital (7, 62, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(8, 62, 226)-Net over F₈₁ — Digital

Digital (8, 62, 226)-net over F₈₁, using

net from sequence [i] based on digital (8, 225)-sequence over F₈₁, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 8 and N(F) ≥ 226, using
  - a curve from the manYPoints database [i]

(8, 62, 3280)-Net in Base 81 — Upper bound on s

There is no (8, 62, 3281)-net in base 81, because

the generalized Rao bound for nets shows that 81^mÂ â‰¥ 21190 818140 497820 045704 455249 697453 024263 248885 843395 882313 346101 757050 970981 863487 787358 705369 689232 383545 693578 101361 > 81⁶² [i]