MinT - Best Known (149−84, 149, s)-Nets in Base 8

Best Known (149−84, 149, s)-Nets in Base 8

(149−84, 149, 110)-Net over F₈ — Constructive and digital

Digital (65, 149, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 51, 45)-net over F₈, using
  - net from sequence [i] based on digital (9, 44)-sequence over F₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 9 and N(F) ≥ 45, using
      - an explicitly constructive algebraic function field [i]
2. digital (14, 98, 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]

(149−84, 149, 150)-Net over F₈ — Digital

Digital (65, 149, 150)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−84, 149, 156)-Net in Base 8

(65, 149, 156)-net in base 8, using

3 times m-reduction [i] based on (65, 152, 156)-net in base 8, using
- base change [i] based on digital (27, 114, 156)-net over F₁₆, using
  - net from sequence [i] based on digital (27, 155)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 27 and N(F) ≥ 156, using
      - a curve from the manYPoints database [i]

(149−84, 149, 3745)-Net in Base 8 — Upper bound on s

There is no (65, 149, 3746)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 366 939439 101287 156183 005456 505873 205245 114388 231612 453530 010271 447038 910292 589304 899970 532551 477501 877457 207685 749106 918813 211902 531904 > 8¹⁴⁹ [i]