Best Known (228, ∞, s)-Nets in Base 4
(228, ∞, 258)-Net over F4 — Constructive and digital
Digital (228, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (228, 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
(228, ∞, 702)-Net in Base 4 — Upper bound on s
There is no (228, m, 703)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (228, 3509, 703)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43509, 703, S4, 5, 3281), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3205 390280 344994 651716 623989 344033 386723 013486 167359 265706 948667 507346 965698 124379 985696 520565 167972 288457 604700 843897 609819 004246 682519 720662 583127 869014 082222 860118 330236 143121 858296 677246 620058 061514 003734 853068 074057 877065 862180 929968 335834 421036 991841 500927 531011 854160 308390 016214 568663 059776 385179 901061 376456 019303 068920 328284 919778 249317 645649 674399 645909 578941 545328 066940 410098 615195 649367 249321 259047 879006 689505 698688 495456 602991 226622 162783 813993 988720 682000 401729 685389 302973 928121 773515 387678 371096 547661 262851 052260 304602 873767 948258 569152 506766 595213 307800 607135 668723 186699 641055 803107 878435 407424 230570 269233 901611 896428 315851 846429 189490 747446 640315 813598 608471 081781 649943 048259 321151 706106 726280 014105 918615 419357 117022 464196 305627 856327 620748 612996 869582 301981 709217 371978 162374 554347 156547 197536 495036 329812 421183 813776 390208 485362 777825 172705 803066 160088 898237 225265 572035 403190 138528 433878 394988 207072 843686 210457 850218 107292 499529 982601 602428 436898 413105 489657 242523 864422 070180 400668 345625 023228 710776 681214 909596 935282 208913 973492 139499 596552 993157 675414 385888 352936 327578 435827 475682 230051 049103 909056 866622 945633 422192 308627 744561 267750 962333 534012 793965 070623 483502 073459 671703 730472 956321 352999 677385 775527 868720 839676 322932 146735 948908 425285 872251 260141 723419 456020 316078 655179 658873 860555 971730 908705 272086 853320 028849 097986 712552 488490 825909 286557 646329 194611 203669 248455 873031 722673 313222 587020 245096 482266 987126 993169 347675 242718 419759 257560 185714 778031 218661 098719 970999 153737 692417 015440 844945 756588 149040 234351 360695 280559 972271 782111 583620 451899 094239 368098 178662 678403 391794 180220 633259 115226 246071 666548 283206 365610 292736 347211 793314 851287 782113 748668 041451 598941 530996 878066 768864 547845 024745 569037 092975 199925 430352 738470 506340 749415 388801 857916 242481 178172 259112 989863 913368 224446 306546 149614 859681 292018 635578 722822 961090 101208 735128 645079 064953 681355 626492 931596 477540 538105 955142 015872 171874 684346 480446 759278 153497 874132 446344 553512 998726 191881 842199 161320 939306 822070 028728 365947 117186 748581 062231 667051 249649 609227 665531 394765 875063 746091 927323 417139 570148 376576 / 547 > 43509 [i]
- extracting embedded OOA [i] would yield OOA(43509, 703, S4, 5, 3281), but