Best Known (199, 199+∞, s)-Nets in Base 4
(199, 199+∞, 200)-Net over F4 — Constructive and digital
Digital (199, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (199, 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
(199, 199+∞, 258)-Net over F4 — Digital
Digital (199, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (199, 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
(199, 199+∞, 614)-Net in Base 4 — Upper bound on s
There is no (199, m, 615)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (199, 3069, 615)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43069, 615, S4, 5, 2870), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 191 961780 359431 816739 182304 904382 517715 681449 677864 530305 551717 179403 220902 533412 811886 137122 634517 783114 544553 303627 768479 109538 030247 204653 410319 642548 020941 991505 311143 472024 465890 894978 823217 765759 476138 096732 060728 328089 577372 067021 605804 684264 658977 945677 318230 328178 677533 695169 100782 211791 357950 523979 770756 068500 227168 964408 332444 757233 672119 830040 294242 258835 714237 288247 302767 665874 557431 741315 929313 492164 290749 397608 520692 771856 073775 783177 905050 767916 129398 452937 236366 190303 773430 145516 132100 715261 430847 028534 107585 453382 174744 552686 542318 899126 330438 155401 782642 380531 163793 055218 950466 899761 925659 086085 118287 884649 568082 137563 467122 839075 016809 107952 988379 417776 209793 254651 468626 223898 954217 691165 744943 671924 895866 261094 036079 785062 510566 342490 079119 229728 405984 287113 544452 588072 305628 652583 262823 386214 148625 082381 501182 379735 365510 553820 479674 164698 244954 237410 392310 330879 597723 042112 215835 411065 639244 413501 136143 300743 843098 884979 470152 586936 523221 684806 830335 432629 034515 812079 288441 005738 986217 036933 554143 169622 682392 322905 294620 500234 683477 016814 104020 925618 159668 780500 893667 330454 218486 268296 577203 638781 863002 634975 880518 143240 571216 232865 440851 773163 371794 046773 856106 869580 244415 981458 256455 970475 004844 024216 646822 152438 587123 142829 989024 881475 882857 034697 877068 218467 060314 855768 279293 041768 730756 857024 358854 466559 575864 533947 258586 849702 396922 599169 717200 356215 942109 734324 457358 043820 553088 916796 480801 283719 159752 837073 007097 383758 835313 946680 424130 415942 965545 578699 005882 478506 439415 925242 919421 701941 630977 177217 419279 862509 502403 351588 835664 707246 398165 066179 921087 890902 902094 093463 663038 849759 288819 007143 200767 348834 566344 798564 171648 854644 848190 097227 464127 132674 736877 284283 888164 925333 380386 994096 365991 815450 551226 617832 079522 411338 982020 810581 897544 425556 118580 132393 863160 216646 390327 558973 423616 / 319 > 43069 [i]
- extracting embedded OOA [i] would yield OOA(43069, 615, S4, 5, 2870), but