Best Known (244, 244+∞, s)-Nets in Base 4
(244, 244+∞, 258)-Net over F4 — Constructive and digital
Digital (244, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (244, 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
(244, 244+∞, 301)-Net over F4 — Digital
Digital (244, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (244, 300)-sequence over F4, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 234 and N(F) ≥ 301, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
(244, 244+∞, 750)-Net in Base 4 — Upper bound on s
There is no (244, m, 751)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (244, 3749, 751)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43749, 751, S4, 5, 3505), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 29594 591628 284653 219340 809300 860528 360907 050943 984913 000302 086530 787505 803569 660270 606242 738492 494801 144710 978286 381919 910285 696302 478536 119775 486737 265865 377868 275879 099015 417293 288994 264124 280618 621294 000740 658108 359499 992204 626544 599030 314745 987224 511736 462030 695105 643887 998639 105918 663309 523851 350816 233566 736814 132333 276672 967658 785728 907176 057558 733521 266719 815069 361699 836269 064685 100240 830153 906792 453179 221202 035204 763857 522611 267917 502769 999101 743094 734276 614816 563878 867814 077600 763464 088921 655092 418268 575200 508627 441759 970208 299966 238742 984455 093389 714350 520266 537656 495318 864679 348393 818188 475374 195850 242056 885858 598678 743833 219183 318397 017719 963840 998862 318628 580463 231287 012351 037130 638305 062941 894880 677480 693012 174368 481803 056531 125775 200732 096704 895771 043305 794350 660116 373279 923999 782378 892274 200455 139814 729903 692919 971334 857364 654958 858788 115003 195865 674035 030322 391414 923162 515727 862674 022971 039188 178972 657051 970096 792397 114961 689793 934413 969614 558240 333104 359511 378529 696581 189514 222944 013082 301839 870680 041476 664482 555015 875308 898266 719251 928010 760184 103479 572019 399902 116873 052984 892570 812513 363583 599263 909172 275976 919563 787313 414232 320134 285382 562218 624326 663460 731483 191229 132688 403810 899596 583327 335071 048192 064568 132941 270805 865243 205262 310806 686070 853030 251471 249860 925045 181147 839472 284672 326538 266953 152135 708798 154719 966522 011449 196422 216544 666949 047974 996176 580994 050538 750351 754928 721857 278990 987069 419657 335443 651059 015359 671947 657729 703979 774991 105293 099294 878926 504204 197957 183306 397771 981436 511253 688998 507983 173273 160811 574874 509581 061865 482619 759694 113200 502901 614090 038164 667733 764924 990719 861765 024239 398792 224460 155585 603410 874817 461196 149488 928251 407582 850942 823662 957481 159406 346613 749865 169767 666852 961948 901341 488345 418977 304195 831399 096106 172147 142181 438505 516374 348887 265853 960638 740511 416966 510502 377113 387064 193464 830256 300580 015405 521612 507055 885569 683748 037276 608746 066599 759409 870712 114077 646446 597971 225706 574401 428758 192281 201007 420996 284081 668660 004751 612697 552731 220820 826944 889115 297447 609706 927113 409987 393260 409457 591824 734658 386859 200589 488631 177604 557802 390549 677705 231867 839875 581134 616658 999884 291868 014455 037714 918579 496644 964405 969583 113487 718466 511639 416310 213603 877517 309848 503577 477120 / 1753 > 43749 [i]
- extracting embedded OOA [i] would yield OOA(43749, 751, S4, 5, 3505), but