MinT - Best Known (81, 81+92, s)-Nets in Base 8

Best Known (81, 81+92, s)-Nets in Base 8

(81, 81+92, 130)-Net over F₈ — Constructive and digital

Digital (81, 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)

(81, 81+92, 216)-Net over F₈ — Digital

Digital (81, 173, 216)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(81, 81+92, 6376)-Net in Base 8 — Upper bound on s

There is no (81, 173, 6377)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 725984 772044 400547 485608 308190 454290 853294 150258 794633 329205 761743 973507 186334 447973 993726 167197 938531 807576 506061 112994 150108 832425 019281 510510 274116 726240 > 8¹⁷³ [i]