MinT - Best Known (49, 49+53, s)-Nets in Base 8

Best Known (49, 49+53, s)-Nets in Base 8

(49, 49+53, 110)-Net over F₈ — Constructive and digital

Digital (49, 102, 110)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (9, 35, 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, 67, 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]

(49, 49+53, 151)-Net over F₈ — Digital

Digital (49, 102, 151)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+53, 4840)-Net in Base 8 — Upper bound on s

There is no (49, 102, 4841)-net in base 8, because

1 times m-reduction [i] would yield (49, 101, 4841)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 16 329017 918476 266943 219270 352842 124026 455376 605208 959542 347863 981239 224457 532043 091881 609232 > 8¹⁰¹ [i]