MinT - Best Known (75, 75+95, s)-Nets in Base 8

Best Known (75, 75+95, s)-Nets in Base 8

(75, 75+95, 130)-Net over F₈ — Constructive and digital

Digital (75, 170, 130)-net over F₈, using

(u,Â u+v)-construction [i] based on
1. digital (14, 61, 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, 109, 65)-net over F₈, using
  - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(75, 75+95, 174)-Net over F₈ — Digital

Digital (75, 170, 174)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+95, 4607)-Net in Base 8 — Upper bound on s

There is no (75, 170, 4608)-net in base 8, because

1 times m-reduction [i] would yield (75, 169, 4608)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 419 733594 927840 297128 305222 277309 758560 643751 302916 903965 813140 966604 468841 122385 048178 999565 763540 855552 593224 388997 214436 683390 550310 547936 996212 700689 > 8¹⁶⁹ [i]