Best Known (247, 247+∞, s)-Nets in Base 3
(247, 247+∞, 120)-Net over F3 — Constructive and digital
Digital (247, m, 120)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (247, 119)-sequence over F3, using
- base reduction for sequences [i] based on digital (64, 119)-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, 119)-sequence over F9, using
(247, 247+∞, 163)-Net over F3 — Digital
Digital (247, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (247, 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
(247, 247+∞, 509)-Net in Base 3 — Upper bound on s
There is no (247, m, 510)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (247, 3052, 510)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(33052, 510, S3, 6, 2805), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 31 846393 707821 294718 655616 171560 108738 269295 938361 733404 929141 400732 811464 110636 625275 270878 590083 798902 523342 491632 661073 143411 113806 496890 470295 077273 794818 412507 343971 730983 123982 297602 998805 749429 688378 745904 023878 900449 225620 652239 789145 071419 676480 319087 154095 508920 333861 974055 991553 355708 356786 294355 072041 452474 366080 600202 618096 441882 635819 522869 531469 962894 263761 164176 466993 748635 060224 099762 200980 514108 312472 728213 122058 574704 926712 220743 713112 548648 983247 900169 688023 925025 258097 128739 384216 862677 288576 175941 394414 978845 911880 428871 968047 425234 407859 006135 008275 555757 459433 592408 106723 078886 661098 661577 550195 837591 778197 005600 877610 913511 855092 967784 362451 667154 213229 618518 486755 371914 458035 503665 945369 060757 998859 918136 040117 924749 993561 847551 518137 536168 304195 449482 249655 928181 527184 109792 188104 457369 246902 713151 079192 972799 117517 695661 212707 108043 038293 635616 109938 060518 086539 520162 348192 086657 429349 642450 050944 972446 016443 699668 808343 889421 583162 993925 437449 940866 640764 306345 768314 332567 257666 765616 465604 807392 115957 199776 362636 106110 596348 519270 123467 843657 723355 925631 629145 165004 405363 204617 318555 033861 638862 269080 881007 364983 612424 340847 446574 950357 037491 248756 851382 778428 154843 888361 376447 690560 038075 061403 357707 558079 418302 575994 660830 194674 782545 411469 849795 261706 432221 729945 842167 607474 834411 846887 636222 634343 697800 883655 079185 694266 685336 931512 825686 840869 269657 345238 459502 515977 272519 133466 176492 861682 576402 450053 / 1403 > 33052 [i]
- extracting embedded OOA [i] would yield OOA(33052, 510, S3, 6, 2805), but