Best Known (247, ∞, s)-Nets in Base 4
(247, ∞, 258)-Net over F4 — Constructive and digital
Digital (247, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (247, 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
(247, ∞, 301)-Net over F4 — Digital
Digital (247, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (247, 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
(247, ∞, 759)-Net in Base 4 — Upper bound on s
There is no (247, m, 760)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (247, 3794, 760)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43794, 760, S4, 5, 3547), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18 268878 418979 498054 659949 817487 936652 451385 842309 889604 793133 653780 329909 341652 871934 658290 283725 510861 123844 555597 736437 565675 139944 302735 134590 471379 079833 235144 864882 175885 448888 645671 622441 070669 386174 085483 024883 036366 710963 311523 867744 479138 821300 602378 826844 246769 381093 441948 254360 090951 916776 913569 863390 534637 656652 598209 938068 535213 385532 588501 844082 328499 231764 497417 986166 197196 775423 279712 663902 770477 873657 009923 673259 106533 811937 880652 272389 774833 352152 980318 462258 403337 923056 294198 558360 367917 824760 643771 337247 819471 725185 965200 209739 456495 449644 534761 161620 039522 920403 517800 968498 149255 606045 751330 025885 075395 598894 319104 283255 160515 949880 672372 318591 623477 509243 643271 000010 655853 165408 656380 783545 732501 237028 681871 220227 107920 563797 555687 064472 742910 962636 881820 169536 843568 051386 022787 219738 496289 897830 052703 533994 269646 267686 754427 950379 240129 419222 727512 928572 602001 265310 667391 353478 352387 513749 613051 938506 011929 399251 995841 465063 034640 592597 816639 796595 888973 488708 156119 596208 645632 180229 612296 715194 670409 318475 325415 051228 489369 721289 105792 797803 010854 724959 211662 930029 535666 844092 118615 803651 504960 464999 005795 886808 104052 593787 179077 854584 521009 601618 931446 071244 508546 809245 749922 546833 540040 540015 193817 521331 346796 354528 353891 637182 867702 159785 307109 435540 656379 894803 285477 012241 555917 050493 673788 169157 588050 369031 956569 802850 254395 685058 404444 521837 127881 765001 746812 245776 585569 357590 366204 422656 218544 854532 150626 226672 315985 855051 354953 986598 834482 334889 067421 638712 464651 335852 940219 032878 981180 602764 673471 672054 884687 119275 680171 745063 210970 179078 672518 423807 648220 472804 219059 771269 782678 304924 177062 803543 084070 731320 211040 951641 462745 655150 814171 982209 095844 823443 905873 707994 967149 569244 980780 500388 822114 006672 934160 088380 453191 787403 366367 532826 157761 208189 397860 397576 212900 425310 289102 767208 665425 482230 713135 166065 097426 581842 352527 742385 459030 665817 665436 144143 289874 220612 342963 849585 947253 858784 479068 103663 719452 619753 259846 272297 226461 966773 192577 928604 555670 906642 064313 210095 670454 826446 535325 524808 469615 635980 836704 780288 099644 273483 518212 559552 201723 679603 006136 306304 908516 480838 191017 149093 796980 304482 360514 567762 164061 590886 983788 107844 939934 103160 746166 837264 089739 594295 443560 035845 826267 294003 895489 791914 934272 / 887 > 43794 [i]
- extracting embedded OOA [i] would yield OOA(43794, 760, S4, 5, 3547), but