Best Known (225, ∞, s)-Nets in Base 4
(225, ∞, 258)-Net over F4 — Constructive and digital
Digital (225, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [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
(225, ∞, 693)-Net in Base 4 — Upper bound on s
There is no (225, m, 694)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (225, 3464, 694)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43464, 694, S4, 5, 3239), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 24038 535193 772609 191820 737324 645859 134607 066828 411635 265272 695617 969196 104629 301912 180549 949803 676470 811473 084648 966105 918262 673058 053667 552716 187358 170509 416680 519024 426538 762151 025947 044361 700969 513707 637940 946853 925446 830066 521431 734785 688177 687782 723425 727972 629737 264663 467948 284734 961243 213579 671500 644904 991376 471852 754882 380082 095383 702430 713914 650593 275938 375632 089237 539075 765671 612929 424318 457559 983458 845325 796042 654105 549214 336812 096775 289773 920439 933865 494054 610291 491029 995974 590523 447931 296266 617792 270761 328896 805600 761457 709091 700462 084508 391338 760335 608100 418565 714604 484601 975522 772828 673729 164747 790553 448123 256902 065995 823803 835505 040688 124895 947592 206987 145266 695731 997939 883490 348486 206202 212402 620586 540753 520175 249052 065743 524026 160732 963120 184641 518042 553327 983164 701139 891821 794432 231276 830921 290146 874250 968835 853264 344219 521514 471982 269235 060669 329712 010724 201940 982013 135744 121286 346207 781015 687070 226447 242493 372108 185733 706837 991117 603029 633012 534811 540635 482820 412111 371345 814043 459289 722659 168245 566270 348406 400514 866677 212228 835182 014022 523981 065171 062351 144981 566590 123101 119861 535111 271482 926421 777428 968886 924553 775766 822802 893720 387410 162458 539629 873851 925485 069714 920708 331391 107145 353387 135832 438440 479576 703999 822029 684819 767848 532743 501621 700684 686657 371780 831760 897275 516127 833267 923916 853789 637224 078962 035514 025848 132553 660103 263217 561377 796838 234145 734709 165594 105125 021878 219876 783106 404574 692162 493445 576076 799321 847659 256768 875152 226767 396401 937264 760896 421591 042227 423919 636222 743321 208421 955853 795161 893782 619966 173548 728816 530999 561360 117472 731702 110596 974442 065710 931556 950856 121273 140851 014706 097449 838634 027702 332488 324687 082202 077510 848243 056468 359216 233107 001612 042321 036634 826757 671017 591386 405532 471679 539007 918316 519602 532211 579808 296580 379489 508220 246951 296542 252161 216081 782806 401322 293639 316557 519622 323105 809055 932962 496768 352442 184709 962749 701363 365088 715128 808266 872858 546316 474977 262347 804048 707219 579797 858372 681189 285656 653332 883540 117680 467172 986872 558005 439724 843932 125766 906970 296790 822241 665128 541821 557582 856192 / 5 > 43464 [i]
- extracting embedded OOA [i] would yield OOA(43464, 694, S4, 5, 3239), but