MinT - Best Known (82, 82+91, s)-Nets in Base 8

Best Known (82, 82+91, s)-Nets in Base 8

(82, 82+91, 130)-Net over F₈ — Constructive and digital

Digital (82, 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)

(82, 82+91, 225)-Net over F₈ — Digital

Digital (82, 173, 225)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(82, 82+91, 7098)-Net in Base 8 — Upper bound on s

There is no (82, 173, 7099)-net in base 8, because

1 times m-reduction [i] would yield (82, 172, 7099)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 215518 615557 057274 876750 920499 024838 704314 791208 793096 604891 415163 158033 874898 662258 078227 643341 075509 441519 774083 717133 932261 933022 251622 009324 959612 544664 > 8¹⁷² [i]