MinT - Best Known (72, 72+75, s)-Nets in Base 8

Best Known (72, 72+75, s)-Nets in Base 8

(72, 72+75, 130)-Net over F₈ — Constructive and digital

Digital (72, 147, 130)-net over F₈, using

13 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, 72+75, 221)-Net over F₈ — Digital

Digital (72, 147, 221)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(72, 72+75, 7639)-Net in Base 8 — Upper bound on s

There is no (72, 147, 7640)-net in base 8, because

1 times m-reduction [i] would yield (72, 146, 7640)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 713182 992483 145204 939274 009254 339213 149261 790964 862634 115341 485225 395136 924745 206991 264313 267103 233921 171570 973489 175877 847598 898946 > 8¹⁴⁶ [i]