Best Known (79, 79+∞, s)-Nets in Base 9
(79, 79+∞, 222)-Net over F9 — Constructive and digital
Digital (79, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (79, 221)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- F4 from the 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) = 79 and N(F) ≥ 222, using
(79, 79+∞, 228)-Net over F9 — Digital
Digital (79, m, 228)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (79, 227)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 228, using
(79, 79+∞, 659)-Net in Base 9 — Upper bound on s
There is no (79, m, 660)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (79, 1976, 660)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91976, 660, S9, 3, 1897), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 48602 686362 124701 582616 704437 997514 326300 933407 237755 025729 293220 218889 623013 328164 475862 058577 501704 181539 773900 958820 489301 053046 637131 021048 827506 388281 126575 028248 267392 878124 247923 520406 075439 319711 788869 065821 546503 320783 504893 890146 274215 370227 867502 606857 599058 605244 713865 757950 961518 246099 704357 983334 729582 806997 343413 566892 509552 910847 952242 844344 793239 127002 114160 135723 651271 388743 985564 953419 806103 063124 398443 651052 998607 728124 936815 854283 469403 513997 556712 250212 711396 755968 125777 636799 517752 254251 683385 786914 542141 291976 408948 423675 320573 252665 207829 699885 126390 234877 825105 405738 244333 686460 567271 113420 095632 479256 083602 000218 697542 624471 080292 512063 539981 561189 373898 338013 884245 246484 746511 388640 347168 128229 392554 747269 217215 229064 887904 262118 056580 902209 031933 480689 053026 645372 557169 287254 434691 085713 711186 776416 466920 586854 334511 739489 982976 108645 425466 898474 954557 799029 797365 450431 789192 957622 011163 597562 607493 320650 296579 330062 492650 257027 243846 304425 146270 008836 917125 303224 598149 151201 816361 531578 453528 021015 119485 270175 198295 440610 696448 647217 423803 182379 118103 634691 178108 961967 211053 745564 295601 425527 949639 649050 057783 520907 628538 740088 265185 360952 071760 030323 215636 128934 437905 039504 499742 004722 221423 542771 602995 319594 102201 353258 166436 513326 066487 219485 407767 877339 852980 551521 281830 979794 732689 226818 578250 718147 378805 801039 642261 212814 988923 002454 182232 961114 141189 417285 333126 787141 627226 956162 047020 809235 535768 922149 384609 381087 962377 204946 667360 622070 653172 292688 634647 801563 521417 538821 402481 907622 589582 775124 000515 532512 244111 904320 892055 467099 404954 668968 407719 333193 069258 794304 029767 007998 850773 315463 845179 638463 028985 989127 454222 501633 929794 904756 660923 422570 149474 370312 309954 899766 506769 824034 651759 283885 288505 666801 106367 959319 970105 364098 327523 374787 720459 407044 917702 944729 781363 879883 738833 246237 321850 765345 601097 874168 795829 / 949 > 91976 [i]
- extracting embedded OOA [i] would yield OOA(91976, 660, S9, 3, 1897), but