Best Known (254, 254+∞, s)-Nets in Base 4
(254, 254+∞, 258)-Net over F4 — Constructive and digital
Digital (254, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (254, 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
(254, 254+∞, 301)-Net over F4 — Digital
Digital (254, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (254, 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
(254, 254+∞, 780)-Net in Base 4 — Upper bound on s
There is no (254, m, 781)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (254, 3899, 781)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43899, 781, S4, 5, 3645), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 59744 572983 117737 022383 779307 858955 854545 020164 332438 683705 724477 230443 209742 961899 807565 722863 765085 884006 878118 136013 777948 588711 542390 979744 804649 586254 048708 787077 805652 455367 875672 434145 085869 147114 494403 201714 675713 995009 274124 943898 076850 382834 576720 878501 163193 438847 027808 741682 115007 623558 054637 834600 645285 865470 617085 931133 953959 374837 766975 877915 947219 598595 913536 350685 548922 455779 297014 152692 448700 039381 664639 428367 880143 315773 617494 677133 528818 435463 254880 762863 388144 523033 490762 173377 652467 030277 765018 639815 554059 153746 325511 101844 210494 182266 430578 223869 627846 215813 918705 615736 050877 032601 327160 659501 788268 143616 032476 218018 119026 391306 415831 079667 816027 203947 465698 423939 146180 129211 514334 877097 259565 839881 587867 324332 703940 141703 333894 567227 401348 664836 589257 615247 186377 198942 816870 029590 382719 894155 720274 220719 388831 515358 524696 810739 875743 663554 010187 740976 627501 632785 100591 126950 186509 925332 152048 173656 627268 264473 729249 867461 491093 713563 531716 121574 591371 869684 231891 298962 888193 221987 892665 686381 266140 266311 266773 591087 651985 171000 185599 465676 570172 868909 942607 283237 535035 812414 412209 384789 035373 738715 442920 579545 264519 148043 738085 739529 558113 012509 581852 218665 430082 613357 191845 804827 682920 456192 025640 586857 468153 482943 017084 424649 091601 457081 630594 175800 191925 698920 544139 313194 325826 447189 430174 550461 469266 529319 283978 436512 489481 490700 340732 693970 486308 768470 697992 434283 238859 494174 887270 519449 961184 365030 358869 119215 406404 708426 062026 693879 289935 762882 738942 551383 855935 706250 797703 327196 892298 669314 370696 982590 218761 445606 731110 513619 315853 973306 417984 364949 649486 609624 378543 625523 699954 456994 619467 345923 015099 206789 564108 207505 878157 828813 815360 665689 832344 542110 516737 593806 762564 123935 520503 740169 592801 526473 205486 339750 083675 313342 111780 227072 072732 072456 532601 716778 111974 991812 611560 112176 387778 771950 190912 431386 267356 996589 943939 202039 670817 386202 367944 992280 539641 498777 348260 252052 845834 027931 420703 294906 663261 424382 553105 682757 995573 447985 444880 816411 036319 257183 313827 985245 669264 624688 425602 173374 147175 721002 041081 070266 999827 733442 114131 878187 687735 622231 439476 832774 880943 248297 423725 799228 459135 069964 516636 508155 774476 792587 403734 392550 624840 640305 657530 843270 375073 187100 001789 031515 608824 836411 221519 543533 330718 901665 238944 992206 083863 468031 457680 861483 970945 263414 272055 050240 / 1823 > 43899 [i]
- extracting embedded OOA [i] would yield OOA(43899, 781, S4, 5, 3645), but