Best Known (250, 250+∞, s)-Nets in Base 4
(250, 250+∞, 258)-Net over F4 — Constructive and digital
Digital (250, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (250, 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
(250, 250+∞, 301)-Net over F4 — Digital
Digital (250, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (250, 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
(250, 250+∞, 768)-Net in Base 4 — Upper bound on s
There is no (250, m, 769)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (250, 3839, 769)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43839, 769, S4, 5, 3589), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 45109 524566 672066 761489 513185 039134 538941 506688 374747 060760 626439 002551 835672 258494 907129 227663 112568 356275 675347 353779 937744 625515 258864 023704 844025 381841 155125 456448 513768 207767 618594 703464 496426 364930 211232 337329 481230 130107 279577 105000 382852 107865 648077 052988 626806 996673 654439 807204 237455 055155 396560 091619 365668 035893 331621 237396 617758 295667 925937 092850 231753 426272 746192 702244 945083 442525 643276 135658 703204 338342 980764 235217 961494 755768 773907 366501 812117 280406 735812 597565 161517 005865 196984 170990 599463 629915 591635 359363 116323 691285 328249 893275 741123 139885 352685 937322 953548 575275 278019 185910 755651 322223 926693 572574 550658 804655 967109 633781 225848 825642 545485 240202 509522 279178 568549 733712 476996 213751 152530 657243 287390 038104 691315 778668 780406 596031 658780 832202 774949 156702 641946 194136 723299 815757 906445 252822 500128 418644 297183 178990 652711 024790 076970 182785 702327 707451 953173 713171 533991 508369 980691 164749 528464 501610 600726 640618 551207 724194 873117 848621 851531 072198 370850 709621 575365 699029 142422 745442 856406 623533 367580 260626 764427 070013 645811 010987 585397 743396 550063 857701 470997 829516 523364 615755 455424 806384 180631 213272 912708 552127 069341 687939 131392 679890 516341 389220 364935 373952 957121 807821 204564 490939 660762 366399 978605 082314 193361 411665 125277 443903 657151 253177 925727 988223 295950 145223 102892 698865 867992 212606 286466 281729 216535 473518 903609 208802 358223 840681 568785 420461 162642 208382 507279 191929 946871 724318 102921 415913 990605 926523 585062 683122 726288 955278 352191 609690 784706 038344 903217 524432 089184 492321 325966 023797 785855 630235 018527 129947 173466 694621 050652 533337 822477 871303 163251 226638 936898 030888 926989 532161 449585 393594 088170 726254 615092 515294 729556 943373 571884 843505 270005 030282 734855 393127 553546 987928 568312 726227 498752 986779 310451 623309 398824 885539 681511 701130 924865 654651 980826 458739 342410 819974 265187 590737 407451 275947 239446 521492 185020 740900 959276 594476 467919 489457 594068 655313 665180 135109 181855 881682 943134 625668 833642 774237 278596 328250 695508 134545 463405 525220 882490 467590 200997 801749 199669 836300 146772 742390 144205 722359 485349 443494 011781 507535 845117 269991 651816 626833 051211 189461 385699 305090 065531 109476 803593 897355 094421 144760 423434 925761 359627 613530 230912 603855 421390 160406 539295 837271 687697 005167 895419 086309 644935 533660 100714 079892 905959 975217 015461 885350 391430 815121 054222 272091 893469 806592 / 1795 > 43839 [i]
- extracting embedded OOA [i] would yield OOA(43839, 769, S4, 5, 3589), but