Best Known (88, ∞, s)-Nets in Base 3
(88, ∞, 63)-Net over F3 — Constructive and digital
Digital (88, m, 63)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (88, 62)-sequence over F3, using
- base reduction for sequences [i] based on digital (13, 62)-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, 62)-sequence over F9, using
(88, ∞, 84)-Net over F3 — Digital
Digital (88, m, 84)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (88, 83)-sequence over F3, using
- t-expansion [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
- t-expansion [i] based on digital (71, 83)-sequence over F3, using
(88, ∞, 189)-Net in Base 3 — Upper bound on s
There is no (88, m, 190)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (88, 943, 190)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3943, 190, S3, 5, 855), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 280 406085 174168 496844 118936 689941 730473 030539 747305 788906 188155 368226 933607 063744 650239 650788 572238 349070 539439 037426 970256 753567 258979 244096 897516 006625 757358 875087 706657 447676 682299 756717 985963 055281 277463 797748 941523 903729 232548 583218 358300 671178 895676 916343 329008 793814 657907 779036 894814 391847 122726 826051 245910 087419 996602 152882 867453 786470 584135 683556 948603 059429 770932 433595 989264 526260 940586 494232 605139 266027 255310 950933 934494 337329 718281 967791 / 214 > 3943 [i]
- extracting embedded OOA [i] would yield OOA(3943, 190, S3, 5, 855), but