Best Known (59, 122, s)-Nets in Base 8
(59, 122, 130)-Net over F8 — Constructive and digital
Digital (59, 122, 130)-net over F8, using
- (u, u+v)-construction [i] based on
- digital (14, 45, 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, 77, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8 (see above)
- digital (14, 45, 65)-net over F8, using
(59, 122, 180)-Net over F8 — Digital
Digital (59, 122, 180)-net over F8, using
(59, 122, 5922)-Net in Base 8 — Upper bound on s
There is no (59, 122, 5923)-net in base 8, because
- 1 times m-reduction [i] would yield (59, 121, 5923)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 18 873672 394104 262683 214850 208967 986455 231346 145574 615329 950495 297371 610869 996252 314522 996202 833611 191779 353440 > 8121 [i]