Best Known (218, ∞, s)-Nets in Base 4
(218, ∞, 200)-Net over F4 — Constructive and digital
Digital (218, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (218, 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
(218, ∞, 258)-Net over F4 — Digital
Digital (218, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (218, 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
(218, ∞, 671)-Net in Base 4 — Upper bound on s
There is no (218, m, 672)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (218, 3354, 672)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43354, 672, S4, 5, 3136), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6 521701 126894 256046 790382 650883 909242 496886 398274 014132 497957 948093 509833 240248 337363 351137 289222 568619 054634 961529 552398 346330 200567 350116 724616 644405 340331 323244 195670 713460 222112 281251 406661 720113 598106 142013 919517 008621 922246 610842 012293 578633 441650 540997 370991 457559 149851 498525 775329 133051 667258 949151 502196 685553 542162 976128 456041 339849 423931 271124 222822 328089 100393 757292 265854 247978 384744 775648 484963 287206 554770 257612 632416 751145 674084 326316 439010 117930 312792 202454 728386 963548 002224 306647 623547 481233 506554 304931 220445 157069 554500 972252 126312 545297 224283 069527 253977 340243 072259 150021 453564 859665 635565 810630 137328 857084 845142 091679 606713 280125 755791 617312 667966 320802 644017 187370 608901 499916 954592 552002 190021 696350 818362 974125 399583 199825 664181 555564 532475 664046 508971 494731 385656 551274 903568 691482 541033 135909 018918 898149 721668 316614 588587 101528 905598 345139 469938 376920 866327 297970 768412 199939 799301 440585 838807 034897 606127 436933 417837 504551 416532 147238 875940 966500 753122 442051 071619 751932 413915 724600 552470 509809 221681 130439 493155 992672 961431 996755 200173 067389 638686 950023 569012 143043 317455 951526 496280 512753 028007 130604 959029 659535 960028 207822 365419 092764 813949 228619 317826 518186 542217 053611 498975 446526 587148 109812 129945 837467 620754 481531 262645 047031 111947 466784 576253 105438 005856 666107 832393 756614 323608 510804 774918 261934 204856 365090 000417 047894 520404 535069 050746 127745 851420 976492 783000 538187 899081 727923 020477 629176 371614 169923 447465 430819 948289 513253 602526 844543 010371 291212 876762 041575 079335 745438 029953 682639 945246 689171 611164 605770 790143 929726 659427 304189 287379 706920 904040 051515 118520 660326 258141 224889 536552 256236 051301 914787 440570 179557 550251 965066 794518 200300 177823 525667 022267 296726 697330 108666 622278 639346 053418 434254 765465 225535 919580 756772 223035 358686 009844 829530 681435 259897 922207 103761 917811 694086 152349 269676 497123 308786 827993 745411 848008 956672 112429 543970 240781 855995 536266 252851 541509 863917 059164 644009 089310 972254 116403 991556 061702 050860 250327 250375 842075 263985 049526 542124 270695 219200 / 3137 > 43354 [i]
- extracting embedded OOA [i] would yield OOA(43354, 672, S4, 5, 3136), but