Best Known (217, 217+∞, s)-Nets in Base 4
(217, 217+∞, 200)-Net over F4 — Constructive and digital
Digital (217, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (217, 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
(217, 217+∞, 258)-Net over F4 — Digital
Digital (217, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (217, 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
(217, 217+∞, 668)-Net in Base 4 — Upper bound on s
There is no (217, m, 669)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (217, 3339, 669)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43339, 669, S4, 5, 3122), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 675 711082 636365 653206 994822 165775 022681 596327 394232 221171 630380 419458 233702 906991 850280 029721 023524 886807 266752 673464 551862 356471 655068 640118 104966 068727 999794 959013 134582 780720 395959 251764 222156 594170 061227 212705 226863 929246 412530 034942 429196 669692 530876 664405 244216 000154 075193 415388 935586 486009 864656 341359 596123 237005 961715 331571 860796 826191 630544 059509 214930 236258 002748 246085 435417 562346 256204 220367 551004 236311 854972 652537 148784 440901 355707 368537 634495 291623 564560 453489 919239 370818 480340 870607 755759 067114 073938 153310 003246 854979 487353 156366 434200 354214 945334 461431 023645 309770 283131 338550 438257 528284 524284 706081 056814 036042 450049 612071 595017 252480 920234 160529 739459 221525 254577 486757 412824 654729 290326 507988 981822 243918 239028 073335 721745 137688 834404 625514 743772 917589 287346 963646 499711 395551 471055 417724 596277 223786 669529 433507 971093 266618 419732 009145 196355 783162 667084 888039 509683 753594 742954 935229 078200 892707 861291 833555 960727 258438 928446 156294 168160 651181 776479 373880 461670 158600 171746 129618 071135 470468 050189 517695 374810 845957 709107 720169 200850 314475 613882 529639 922010 889390 532486 991555 492370 023692 689097 527204 422087 669187 869922 838523 567782 826943 465391 239231 034975 204522 822238 642957 826747 758574 095571 810456 756714 001856 238091 754049 816109 305576 392692 962858 084734 231032 531855 609247 602107 100650 997651 203855 407840 411207 833938 896823 944775 961583 989110 382520 961579 425662 658649 228258 031032 639389 958986 894603 607097 856175 180651 476486 904617 775216 261417 771428 122379 211209 044895 558999 761758 509494 866968 249182 753359 600883 752430 969564 159115 935062 749369 435012 716345 658610 445715 106146 615922 818845 672957 348690 308093 522951 210114 424080 533383 885641 309747 491127 591051 604391 509230 354503 626143 358084 170955 447904 977236 651671 191653 785446 405875 149414 355681 101645 024499 242073 905988 774178 375195 389444 562827 502645 840563 498105 709944 193729 531533 054154 784284 766307 384677 326804 599076 674383 218396 855306 353221 430153 853242 732121 990640 302872 278701 850001 543822 368617 342641 263520 764134 880725 168020 611817 807803 493284 090303 926110 975283 953664 / 347 > 43339 [i]
- extracting embedded OOA [i] would yield OOA(43339, 669, S4, 5, 3122), but