MinT - Best Known (77, 77+96, s)-Nets in Base 8

Best Known (77, 77+96, s)-Nets in Base 8

(77, 77+96, 130)-Net over F₈ — Constructive and digital

Digital (77, 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)

(77, 77+96, 195)-Net over F₈ — Digital

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]

(77, 77+96, 4784)-Net in Base 8 — Upper bound on s

There is no (77, 173, 4785)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 724702 211239 106104 081092 618352 616809 849219 308147 257698 383453 414507 066559 363887 186822 150250 476164 914069 502271 744060 751348 632214 902119 633193 099002 860356 703685 > 8¹⁷³ [i]