Best Known (79, 79+132, s)-Nets in Base 3
(79, 79+132, 54)-Net over F3 — Constructive and digital
Digital (79, 211, 54)-net over F3, using
- net from sequence [i] based on digital (79, 53)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 53)-sequence over F9, using
- s-reduction based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- s-reduction based on digital (13, 63)-sequence over F9, using
- base reduction for sequences [i] based on digital (13, 53)-sequence over F9, using
(79, 79+132, 84)-Net over F3 — Digital
Digital (79, 211, 84)-net over F3, using
- t-expansion [i] based on digital (71, 211, 84)-net over F3, using
- net from sequence [i] based on digital (71, 83)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 71 and N(F) ≥ 84, using
- net from sequence [i] based on digital (71, 83)-sequence over F3, using
(79, 79+132, 362)-Net over F3 — Upper bound on s (digital)
There is no digital (79, 211, 363)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(3211, 363, F3, 132) (dual of [363, 152, 133]-code), but
- residual code [i] would yield OA(379, 230, S3, 44), but
- 2 times truncation [i] would yield OA(377, 228, S3, 42), but
- the linear programming bound shows that M ≥ 5912 215514 524704 110906 945136 883000 212719 987869 884535 855049 744419 389403 700722 336619 158801 044684 / 1072 032675 663595 149019 556086 689047 982002 296477 532875 566121 > 377 [i]
- 2 times truncation [i] would yield OA(377, 228, S3, 42), but
- residual code [i] would yield OA(379, 230, S3, 44), but
(79, 79+132, 364)-Net in Base 3 — Upper bound on s
There is no (79, 211, 365)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 51954 847099 737385 378336 455060 931607 559991 263664 518809 948792 206785 285144 079650 838704 621468 610287 455841 > 3211 [i]