Best Known (246, ∞, s)-Nets in Base 3
(246, ∞, 119)-Net over F3 — Constructive and digital
Digital (246, m, 119)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (246, 118)-sequence over F3, using
- base reduction for sequences [i] based on digital (64, 118)-sequence over F9, using
- s-reduction based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- s-reduction based on digital (64, 164)-sequence over F9, using
- base reduction for sequences [i] based on digital (64, 118)-sequence over F9, using
(246, ∞, 163)-Net over F3 — Digital
Digital (246, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (246, 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
(246, ∞, 507)-Net in Base 3 — Upper bound on s
There is no (246, m, 508)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (246, 3040, 508)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(33040, 508, S3, 6, 2794), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 24 020412 570680 057773 915367 262295 144330 302771 296866 274929 171900 589888 227301 704595 423024 168366 833231 241635 142175 673081 434993 344495 055280 812573 259264 772023 432697 116210 181710 748616 047064 508736 999861 194175 377784 301406 089999 658699 437768 280018 254712 897065 537254 547821 600585 194598 582856 985639 317052 201858 703255 618300 586597 444356 821662 235471 516545 227310 365804 126619 653891 476947 872388 949446 034575 400313 207194 554690 509151 619351 195943 985178 412702 759244 797644 326670 974083 560435 825545 082685 430158 597275 168342 968272 795798 100266 965539 896708 290297 313293 667027 771827 765794 241265 619266 861095 653069 250424 023445 396682 043446 070556 123626 306540 375123 902407 772736 199216 110855 074366 640886 365342 582042 170874 768080 909730 180080 009134 574483 710650 859489 534945 497255 838712 318258 166364 517772 148130 571726 785442 281719 939116 046671 459917 748211 722056 971095 659372 474694 034446 226823 392813 253405 920373 433907 709615 666144 738721 411700 946398 432193 987909 038668 015665 550008 548390 527442 177471 920105 189908 405729 400583 959623 800505 051143 960277 436536 227688 690640 078546 171685 591794 533387 451794 256800 686082 680928 964757 976302 177691 609140 723152 097634 623448 042859 147741 892695 936632 865348 721578 761865 294267 822877 430475 435879 921799 651088 126901 389855 182386 575632 621802 202748 930720 149742 464818 455637 424623 627059 752027 796050 640021 213709 307638 623692 115511 683202 274269 638698 074155 430822 819784 769000 642162 376187 579087 684121 215842 382610 135258 117669 265497 758476 778668 577826 242439 411450 193313 994696 210600 518347 245153 424855 / 559 > 33040 [i]
- extracting embedded OOA [i] would yield OOA(33040, 508, S3, 6, 2794), but