Best Known (227, 227+∞, s)-Nets in Base 4
(227, 227+∞, 258)-Net over F4 — Constructive and digital
Digital (227, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (227, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second 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) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
(227, 227+∞, 699)-Net in Base 4 — Upper bound on s
There is no (227, m, 700)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (227, 3494, 700)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43494, 700, S4, 5, 3267), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4 481837 713402 374741 113927 921781 061698 623875 173759 173256 980302 048973 458472 217234 041946 715891 795734 552066 909056 059733 660766 053392 464444 007067 150671 149611 092576 559788 221307 873708 615874 471215 322700 061988 058151 953749 508184 202367 225632 215779 309479 886034 288503 857802 621858 566775 756778 281343 061916 330754 740707 190465 233298 769825 762006 864015 441003 985508 114799 693394 082273 746491 547967 061928 792760 576055 305472 750184 894064 172300 793670 899043 155346 007551 486621 870563 283104 954938 633772 587120 500879 699046 822959 742263 793741 325578 636625 619290 889889 464623 231101 239279 728625 266950 661224 841074 042614 220319 165899 262654 463122 114784 191574 027120 767572 283004 478087 956127 234220 956640 559545 203802 328365 315918 844342 153721 634183 234082 519755 262493 856211 674500 801062 858943 228920 469878 190448 239468 768602 054863 040656 428555 419516 726557 313599 859635 095425 280300 625050 696928 217232 873166 414770 021847 513590 174730 934950 224947 516017 147084 871100 013829 607362 315897 549013 923975 983400 202020 863067 940635 250842 165396 997164 797773 554355 800347 646039 421217 377988 730988 645000 100279 823739 979936 960821 189999 751600 895242 396899 340882 104997 601049 838097 924048 929345 994988 244269 509841 262613 702779 138226 636458 061928 683727 420563 987549 346889 587176 988958 573536 186930 064334 734976 508289 728456 465397 475640 451969 613435 396066 858403 672597 793888 685547 186474 882064 904523 809593 350028 287369 655630 678946 364024 568023 039445 486404 714630 250903 772117 302769 001227 948359 646881 740167 926716 872745 724555 572102 780091 345198 365044 380161 965295 844972 687458 136831 851779 315435 667421 870520 961394 013514 810241 797197 610215 784221 569649 867487 060386 961405 433597 781654 185036 615180 343685 397199 781157 865806 907820 469187 833235 391290 716736 051402 878745 645107 515657 590938 561011 792224 839798 663643 226772 907714 879730 674120 847622 406417 423256 671150 039555 566663 609168 311411 993261 807878 778057 111407 577901 516853 884442 646389 066145 987501 803733 775568 817514 111005 233267 936182 970603 828651 857721 167589 576863 312591 716547 462734 966895 277738 610555 682090 737016 964578 504704 621044 718464 642394 758476 243225 010327 560924 169043 244835 228254 834925 305417 691019 638540 628547 317518 126074 311477 986901 301087 309758 771204 578577 301389 105516 382248 763392 / 817 > 43494 [i]
- extracting embedded OOA [i] would yield OOA(43494, 700, S4, 5, 3267), but