Best Known (241, 241+∞, s)-Nets in Base 4
(241, 241+∞, 258)-Net over F4 — Constructive and digital
Digital (241, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (241, 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
(241, 241+∞, 301)-Net over F4 — Digital
Digital (241, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (241, 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
(241, 241+∞, 741)-Net in Base 4 — Upper bound on s
There is no (241, m, 742)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (241, 3704, 742)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43704, 742, S4, 5, 3463), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5 992660 668231 385371 637621 644251 796663 153404 296286 514412 657347 748051 186637 727376 141320 072219 824979 643709 512585 665362 253796 927234 072687 280265 173214 182105 592356 683135 592429 870213 487959 106733 811313 546744 713279 508848 599974 924936 744918 222403 618046 831165 555088 570955 159098 578128 496757 476318 653812 519841 679760 740361 271228 139340 944184 097535 142380 889985 149719 019990 969518 549288 121419 505470 149748 768130 041455 271521 483055 507900 323661 587935 351701 134612 302557 926737 469974 094304 920762 795589 578055 419589 394247 261454 670857 279877 599067 661269 441800 437785 398186 137317 567360 767756 328786 885008 807627 882224 960517 013972 028287 515516 855797 129702 050489 784144 986501 008146 260047 542042 201529 430965 527849 627699 318502 871219 066344 864999 165009 970967 799069 025953 994330 325357 678668 193686 119799 635865 743329 276682 018858 141921 731030 250044 723137 825433 809317 049330 844128 851302 239616 819389 960092 849769 449181 258942 796743 220635 279899 360050 659891 812983 130074 943746 126122 163804 670531 305491 920538 120098 734732 031552 454635 490863 550513 389212 155192 739589 319337 114334 803780 827132 000401 954026 195239 609012 913196 638863 501301 027539 247746 637445 422649 904785 848604 079453 477038 427608 360744 684234 871544 525335 285139 462116 152200 908872 532080 130537 205966 838383 272647 233535 250380 528476 584440 846227 303247 422533 492620 819314 331334 814580 051827 295364 229259 785692 546725 519659 427401 750149 857303 826539 003299 165718 723181 618497 617615 051874 535423 214222 131789 797971 442454 791554 303687 812592 068121 338315 789044 922483 905111 421772 001701 822026 098801 761279 589654 610023 018778 122608 752109 524395 649381 485235 039385 503389 835802 103854 180892 008508 064428 049339 204977 925038 650910 635108 115013 105005 663104 397393 857760 615656 883144 136163 318107 861215 867477 322773 558713 957587 147826 931602 289493 923505 601712 144263 374991 939404 813410 477167 936586 198569 533086 597591 144007 894233 125838 494628 893813 980609 666587 819657 190528 503609 766836 648389 906434 360171 676681 606584 595663 453852 456137 774164 720388 000358 604064 182020 023014 081477 950409 601980 498938 970911 627079 982572 436996 746461 107837 162521 404529 648089 824902 250044 054724 095621 705348 128241 917462 802791 167874 686038 577077 396581 338169 439119 604223 093542 118754 743387 179393 292810 855228 362248 830407 013330 218556 604093 955407 621211 468595 000491 983122 778374 498323 689245 655708 966676 175112 661607 222636 227910 959104 / 433 > 43704 [i]
- extracting embedded OOA [i] would yield OOA(43704, 742, S4, 5, 3463), but