MinT - Best Known (35, 35+106, s)-Nets in Base 8

Best Known (35, 35+106, s)-Nets in Base 8

(35, 35+106, 65)-Net over F₈ — Constructive and digital

Digital (35, 141, 65)-net over F₈, using

t-expansion [i] based on digital (14, 141, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(35, 35+106, 112)-Net over F₈ — Digital

Digital (35, 141, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(35, 35+106, 710)-Net in Base 8 — Upper bound on s

There is no (35, 141, 711)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 22 717560 399169 178417 556511 917480 091401 335173 673454 718882 261053 464131 661732 548735 666494 249363 495819 752533 789305 415411 297380 522664 > 8¹⁴¹ [i]