MinT - Best Known (72, 153, s)-Nets in Base 8

Best Known (72, 153, s)-Nets in Base 8

(72, 153, 130)-Net over F₈ — Constructive and digital

Digital (72, 153, 130)-net over F₈, using

7 times m-reduction [i] based on digital (72, 160, 130)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (14, 58, 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, 102, 65)-net over F₈, using
    - net from sequence [i] based on digital (14, 64)-sequence over F₈ (see above)

(72, 153, 198)-Net over F₈ — Digital

Digital (72, 153, 198)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 153, 6062)-Net in Base 8 — Upper bound on s

There is no (72, 153, 6063)-net in base 8, because

1 times m-reduction [i] would yield (72, 152, 6063)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 186974 755920 596093 667414 717319 864469 628003 461468 003437 686995 004359 293618 548963 772057 824042 045809 200390 368442 122969 966455 977936 382456 137167 > 8¹⁵² [i]