MinT - Best Known (155−85, 155, s)-Nets in Base 8

Best Known (155−85, 155, s)-Nets in Base 8

(155−85, 155, 130)-Net over F₈ — Constructive and digital

Digital (70, 155, 130)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (14, 56, 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]
2. digital (14, 99, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(155−85, 155, 173)-Net over F₈ — Digital

Digital (70, 155, 173)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(155−85, 155, 4804)-Net in Base 8 — Upper bound on s

There is no (70, 155, 4805)-net in base 8, because

1 times m-reduction [i] would yield (70, 154, 4805)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11 959580 110068 350029 547049 620339 667942 131213 415561 806000 072647 434908 528688 615555 863034 294432 836258 210936 653026 238357 894037 546511 833284 545104 > 8¹⁵⁴ [i]