Best Known (122−67, 122, s)-Nets in Base 8
(122−67, 122, 100)-Net over F8 — Constructive and digital
Digital (55, 122, 100)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (8, 41, 35)-net over F8, using
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F8 with g(F) = 7, N(F) = 34, and 1 place with degree 2 [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using a function field by Sémirat [i]
- net from sequence [i] based on digital (8, 34)-sequence over F8, using
- digital (14, 81, 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 (8, 41, 35)-net over F8, using
(122−67, 122, 144)-Net over F8 — Digital
Digital (55, 122, 144)-net over F8, using
- t-expansion [i] based on digital (45, 122, 144)-net over F8, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 45 and N(F) ≥ 144, using
- net from sequence [i] based on digital (45, 143)-sequence over F8, using
(122−67, 122, 3830)-Net in Base 8 — Upper bound on s
There is no (55, 122, 3831)-net in base 8, because
- 1 times m-reduction [i] would yield (55, 121, 3831)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 18 880216 592050 286322 744240 886193 496913 256663 456762 096805 495512 714275 869994 584013 292623 160206 840357 727288 702890 > 8121 [i]