Best Known (200, 200+∞, s)-Nets in Base 3
(200, 200+∞, 112)-Net over F3 — Constructive and digital
Digital (200, m, 112)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (200, 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
(200, 200+∞, 163)-Net over F3 — Digital
Digital (200, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (200, 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
(200, 200+∞, 414)-Net in Base 3 — Upper bound on s
There is no (200, m, 415)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (200, 2483, 415)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32483, 415, S3, 6, 2283), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 654034 186930 797461 099077 410386 650735 789998 859821 284260 560629 588107 008994 763078 207842 003384 583785 994242 086802 453801 845119 610893 027219 679837 422700 110011 117675 141748 149475 972421 523760 901708 252784 320815 387062 432222 892497 403013 075153 634338 660361 988001 249977 450570 940169 138719 979170 396572 388157 565603 675621 234802 648514 332494 387617 363368 204835 332012 025896 117489 844822 522051 768136 928353 885715 620702 607094 292176 711030 933874 142829 615777 126581 340638 604678 007326 879577 721422 716351 548276 376747 284665 839468 223059 482302 871216 895401 383190 589833 289834 496064 470800 596864 120290 743884 631425 651361 421378 829935 925288 664970 255227 369955 042768 927927 793392 965886 053339 181932 271188 866605 333124 337834 838973 475619 331511 916841 855282 584134 683422 073949 550519 999396 059765 573587 454504 999654 239100 212512 059989 583912 967374 348258 008800 417334 695259 288529 431465 828808 753384 215494 184321 024093 033809 191110 758103 835217 820247 033499 317513 033360 288627 208987 861242 646104 436928 509967 036936 193398 903656 037632 712886 375369 953582 543436 597777 609039 952228 040671 992826 100908 548629 508407 401156 076553 490232 751685 801886 528770 215547 801261 027905 033228 865552 161472 541910 284929 975485 749392 578801 960164 470160 184012 278446 660321 676987 607783 723088 440683 / 1142 > 32483 [i]
- extracting embedded OOA [i] would yield OOA(32483, 415, S3, 6, 2283), but