Best Known (221, 221+∞, s)-Nets in Base 4
(221, 221+∞, 200)-Net over F4 — Constructive and digital
Digital (221, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (221, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(221, 221+∞, 258)-Net over F4 — Digital
Digital (221, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (221, 257)-sequence over F4, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 191 and N(F) ≥ 258, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
(221, 221+∞, 680)-Net in Base 4 — Upper bound on s
There is no (221, m, 681)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (221, 3399, 681)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43399, 681, S4, 5, 3178), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 8043 199418 175352 949318 273086 392326 950311 872122 991684 830538 435970 227808 264853 518584 526447 959094 845493 575777 637473 405029 102916 256941 398472 795618 641356 991758 947070 025831 131928 528478 676080 471741 656365 214639 614904 489925 685075 012811 339936 791737 346168 392041 897544 208509 527362 819192 463770 114256 356024 122198 079564 337686 611953 067257 126498 666129 461674 815136 622218 594196 596760 961392 213908 405880 343919 776919 718209 248178 232863 915898 325513 946339 524476 208650 365849 836431 250402 405630 057940 398967 653605 476065 431682 205411 900615 529885 533386 473728 177627 021095 332291 470258 143443 755097 817165 750003 102261 098407 191045 819202 154757 806254 521564 694387 624719 920592 027855 618322 002551 960233 985930 940881 849659 784931 001422 714911 992843 266736 098114 651291 311422 570093 963403 165621 515390 164008 440309 823034 947824 285147 113426 994793 955831 130269 582316 002808 228071 247059 978441 112736 868365 670906 564886 961690 620946 300062 696520 923840 039661 254262 493967 582080 087298 873034 606473 533253 521917 485942 667314 764014 854988 524171 549018 150737 279325 562902 604972 923838 851783 347721 145661 906069 269938 359767 673462 901710 859851 608390 672942 129226 740663 665957 342021 773152 226823 302454 514146 203066 032849 500700 508534 168649 575282 901162 530940 906094 919336 353905 607521 847205 177051 611233 193890 501658 498671 194156 312825 218817 175742 469143 933000 797322 303255 989820 479441 675033 033721 412867 341541 121063 483942 689464 419042 130376 655825 915542 378305 704463 562372 190537 864353 346557 566678 233127 844898 070547 436284 215163 048926 575855 100868 971932 720560 166359 751112 631651 870749 357265 386213 457499 322313 834795 500718 006654 570276 731090 385497 700624 694888 051876 127575 923052 230362 097441 696957 044327 441490 854164 070194 113998 525136 384120 524753 009558 835753 597059 341727 019001 470837 614793 557510 267075 076365 860273 653574 218140 097742 291913 841717 269871 246391 092278 063478 235435 300364 401384 987038 303833 982341 459090 097125 431714 977450 968937 489668 177935 870403 230765 857511 341074 931030 875267 213150 634815 572805 741590 861369 621493 361232 479334 837035 426391 932007 188179 684815 313564 239705 697446 522111 917862 352652 757996 053787 384045 653603 996843 042317 210952 249180 809016 457320 988672 / 3179 > 43399 [i]
- extracting embedded OOA [i] would yield OOA(43399, 681, S4, 5, 3178), but