MinT - Best Known (77, 77+95, s)-Nets in Base 8

Best Known (77, 77+95, s)-Nets in Base 8

(77, 77+95, 130)-Net over F₈ — Constructive and digital

Digital (77, 172, 130)-net over F₈, using

t-expansion [i] based on digital (76, 172, 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, 110, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(77, 77+95, 195)-Net over F₈ — Digital

Digital (77, 172, 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]

(77, 77+95, 5036)-Net in Base 8 — Upper bound on s

There is no (77, 172, 5037)-net in base 8, because

1 times m-reduction [i] would yield (77, 171, 5037)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 26845 338179 644435 040411 667078 650543 836229 710026 490314 676149 853748 363851 264817 707414 523693 956510 335062 233278 877037 036251 179587 361215 382463 392173 670672 914560 > 8¹⁷¹ [i]