Best Known (79, 225, s)-Nets in Base 3
(79, 225, 54)-Net over F3 — Constructive and digital
Digital (79, 225, 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, 225, 84)-Net over F3 — Digital
Digital (79, 225, 84)-net over F3, using
- t-expansion [i] based on digital (71, 225, 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, 225, 283)-Net over F3 — Upper bound on s (digital)
There is no digital (79, 225, 284)-net over F3, because
- 2 times m-reduction [i] would yield digital (79, 223, 284)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(3223, 284, F3, 144) (dual of [284, 61, 145]-code), but
- residual code [i] would yield OA(379, 139, S3, 48), but
- the linear programming bound shows that M ≥ 50 288774 556502 552979 660125 115218 456368 310549 423022 168918 582978 795551 485882 074444 648171 632226 289738 754149 887332 083901 197203 302095 178151 432355 680080 363765 867057 861079 113887 498268 062169 307278 067781 076899 786375 278313 / 1 005522 717306 856140 949852 324268 723746 442220 079713 834760 775274 718454 197834 327923 327924 500288 387852 716262 070035 331120 864819 171639 324760 829355 613325 385992 572938 220356 162952 927625 > 379 [i]
- residual code [i] would yield OA(379, 139, S3, 48), but
- extracting embedded orthogonal array [i] would yield linear OA(3223, 284, F3, 144) (dual of [284, 61, 145]-code), but
(79, 225, 346)-Net in Base 3 — Upper bound on s
There is no (79, 225, 347)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 261553 601870 068029 881204 205087 506603 205940 264388 917991 234715 326997 876062 205062 605119 565088 706992 281192 429287 > 3225 [i]