MinT - Best Known (78, 78+95, s)-Nets in Base 8

Best Known (78, 78+95, s)-Nets in Base 8

(78, 78+95, 130)-Net over F₈ — Constructive and digital

Digital (78, 173, 130)-net over F₈, using

t-expansion [i] based on digital (76, 173, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 62, 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, 111, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(78, 78+95, 195)-Net over F₈ — Digital

Digital (78, 173, 195)-net over F₈, using

t-expansion [i] based on digital (77, 173, 195)-net over F₈, using
- net from sequence [i] based on digital (77, 194)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 77 and N(F) ≥ 195, using
    - Drinfeld modules of rank 1 [i]

(78, 78+95, 5266)-Net in Base 8 — Upper bound on s

There is no (78, 173, 5267)-net in base 8, because

1 times m-reduction [i] would yield (78, 172, 5267)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 216298 324902 442967 532832 511437 408671 248218 650022 404941 073788 304396 699080 460332 395398 262657 909116 333190 358879 722167 132406 730182 909003 017000 475293 116610 025024 > 8¹⁷² [i]