Best Known (72, 168, s)-Nets in Base 8
(72, 168, 111)-Net over F8 — Constructive and digital
Digital (72, 168, 111)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (10, 58, 46)-net over F8, using
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 9, N(F) = 45, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 9 and N(F) ≥ 45, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (10, 45)-sequence over F8, using
- digital (14, 110, 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 (10, 58, 46)-net over F8, using
(72, 168, 158)-Net over F8 — Digital
Digital (72, 168, 158)-net over F8, using
(72, 168, 162)-Net in Base 8
(72, 168, 162)-net in base 8, using
- base change [i] based on digital (30, 126, 162)-net over F16, using
- net from sequence [i] based on digital (30, 161)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 30 and N(F) ≥ 162, using
- net from sequence [i] based on digital (30, 161)-sequence over F16, using
(72, 168, 3846)-Net in Base 8 — Upper bound on s
There is no (72, 168, 3847)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 52 496296 221341 058866 495775 462292 186684 273489 399023 566710 597733 200612 620025 228839 524494 561497 926946 998921 973422 875256 769743 155994 564740 826596 038843 663984 > 8168 [i]