Best Known (192, 192+∞, s)-Nets in Base 3
(192, 192+∞, 112)-Net over F3 — Constructive and digital
Digital (192, m, 112)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (192, 111)-sequence over F3, using
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on function field F4/F3 with g(F4) = 79, N(F4) ≥ 2, and N(F4) + N2(F4) ≥ 112 from GarcÃa–Stichtenoth tower as constant field extension [i]
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
(192, 192+∞, 163)-Net over F3 — Digital
Digital (192, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (192, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
(192, 192+∞, 398)-Net in Base 3 — Upper bound on s
There is no (192, m, 399)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (192, 2387, 399)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32387, 399, S3, 6, 2195), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 11 524478 558889 955649 813697 563192 787731 313338 650961 538439 354658 994727 674518 433385 059896 198887 127844 184365 275728 825359 035909 115773 204878 673198 228343 478548 233523 817373 059698 871609 403260 659457 669793 415018 029881 090403 287635 903781 652754 564798 835031 765501 181369 194532 095660 108652 013863 267353 999338 508080 286900 289130 396998 834334 068074 054602 275589 389948 366746 275850 040907 323996 754164 059606 840352 922307 942288 717723 468904 502461 996411 036594 506804 945431 642947 676893 652268 229472 459615 154284 099733 251179 019458 999863 945700 056789 782691 019157 926401 722158 722134 597257 228086 856242 604371 196359 345169 040658 010236 573305 472326 367997 442171 961029 990058 472262 527212 680009 472447 215845 609488 536987 594391 311759 595687 360097 589119 466821 293379 488532 380016 271035 832477 436637 617322 501366 214347 255322 831119 983702 635931 793679 673090 082201 457164 527579 708688 711938 303478 493922 274566 488652 228738 967515 765008 152545 113644 745244 163955 841829 644042 507537 194445 509660 818984 126397 879250 487264 021998 986389 382899 080957 768246 684896 587649 704849 929728 856678 386371 023144 178035 827676 947128 910308 176668 961460 700644 673816 616748 676726 918047 700017 973646 776574 519648 942703 927195 754147 629806 114709 132663 / 122 > 32387 [i]
- extracting embedded OOA [i] would yield OOA(32387, 399, S3, 6, 2195), but