Best Known (72, 72+84, s)-Nets in Base 8
(72, 72+84, 130)-Net over F8 — Constructive and digital
Digital (72, 156, 130)-net over F8, using
- 4 times m-reduction [i] based on digital (72, 160, 130)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 58, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction 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]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- digital (14, 102, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8 (see above)
- digital (14, 58, 65)-net over F8, using
- (u, u+v)-construction [i] based on
(72, 72+84, 187)-Net over F8 — Digital
Digital (72, 156, 187)-net over F8, using
(72, 72+84, 193)-Net in Base 8
(72, 156, 193)-net in base 8, using
- base change [i] based on digital (33, 117, 193)-net over F16, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 33 and N(F) ≥ 193, using
- net from sequence [i] based on digital (33, 192)-sequence over F16, using
(72, 72+84, 5307)-Net in Base 8 — Upper bound on s
There is no (72, 156, 5308)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 766 017656 749250 137844 435714 760212 879188 361837 669400 767673 606869 590914 640490 462401 862228 497497 549553 855804 185568 779581 961951 661953 522980 415759 > 8156 [i]