Best Known (210, 210+∞, s)-Nets in Base 4
(210, 210+∞, 200)-Net over F4 — Constructive and digital
Digital (210, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (210, 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
(210, 210+∞, 258)-Net over F4 — Digital
Digital (210, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (210, 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
(210, 210+∞, 647)-Net in Base 4 — Upper bound on s
There is no (210, m, 648)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (210, 3234, 648)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43234, 648, S4, 5, 3024), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 728063 548606 792354 118578 864999 438365 106683 077304 021871 879532 880246 570646 988510 025343 623715 018378 837295 255941 626898 245632 547962 972170 868813 427604 212817 053094 204063 128466 919435 570817 362464 896364 963145 266598 641797 859509 467693 392653 139751 184660 089513 966691 427169 247644 684121 944875 603070 749293 412757 987474 945771 416457 269414 910021 185425 148847 906322 401535 563234 969811 954060 904071 134813 993995 969256 102920 019277 269283 865510 303504 917081 025468 712213 383261 831111 519764 860692 122852 393586 077014 296190 384851 636702 865561 318359 294418 520274 830430 763913 018815 490646 701339 277857 080185 877910 553961 175256 206394 389326 416347 477565 030857 413913 505929 834237 175880 502004 898592 326632 353367 876705 454403 603422 994755 139818 948835 770798 392452 231814 934735 799703 848392 785381 073803 123573 796002 643394 613408 934584 733723 637965 326406 369177 359294 226998 434896 771306 178221 354031 836482 629239 853334 730067 992827 645867 029705 007258 106065 000518 290978 242695 348179 386419 242228 507057 741500 239959 421313 185354 879296 530187 994539 040092 788419 386430 972186 696084 764486 313871 476200 157690 928356 397301 301350 137676 120458 133000 307812 423338 761054 601136 606429 685731 608479 591434 618259 596090 032998 839839 285179 196798 076555 178857 950666 878391 612818 327988 908225 896974 579613 324982 455770 729848 341714 020235 163676 265844 115844 830944 622262 826913 290343 297659 875214 094165 227845 477479 969408 904006 053633 312110 184091 187695 079741 603390 755386 844545 715054 803233 454512 377747 075622 146374 133961 930657 473551 701019 831179 593217 249776 769020 664150 610886 641028 914742 001250 207655 059733 072893 586231 591664 271980 962584 876214 834151 228991 981230 812877 820113 966673 891475 083955 742440 937175 025503 098306 770139 425237 513080 164629 596843 254296 220929 074986 632210 429397 222634 211525 921808 685908 478449 483923 506746 499495 051057 358995 347363 977968 586370 132779 073264 084283 071868 467973 203686 185994 361090 229486 459688 227334 532465 867113 189862 880264 214867 040269 569214 887162 691973 252577 671728 252772 954823 270796 873452 785306 248725 728747 080472 941306 142286 599891 728967 651234 414592 / 3025 > 43234 [i]
- extracting embedded OOA [i] would yield OOA(43234, 648, S4, 5, 3024), but