Best Known (187, ∞, s)-Nets in Base 4
(187, ∞, 200)-Net over F4 — Constructive and digital
Digital (187, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (187, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the 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) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(187, ∞, 220)-Net over F4 — Digital
Digital (187, m, 220)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (187, 219)-sequence over F4, using
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 181 and N(F) ≥ 220, using
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
(187, ∞, 578)-Net in Base 4 — Upper bound on s
There is no (187, m, 579)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (187, 2889, 579)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42889, 579, S4, 5, 2702), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 248 802481 087448 923873 487876 583149 788609 150452 076500 020070 576166 568824 062587 448074 029334 547846 673077 906162 639358 443202 670391 015426 774550 502382 725264 964021 834725 609371 135380 395283 938966 130712 072478 246384 926553 973849 288067 096490 757305 850664 518640 502417 128185 354903 602398 911791 172278 131238 736597 258698 096337 770353 202197 282645 561466 630550 004117 644901 030975 844310 439743 957949 427227 641874 656278 847579 935139 920451 196141 701659 504090 926364 381773 648314 985646 295215 962994 537168 868749 422208 533437 983505 111170 943058 145416 591200 465660 510331 178875 920898 357867 119021 267309 831693 823156 290689 550083 517063 033108 794669 657136 852127 497857 958828 258741 539059 282393 980588 807527 917952 035538 420384 841993 620117 860432 478348 776210 687629 008179 613447 368920 896562 776481 848780 543246 786861 363863 487693 869977 123827 649219 041041 434116 961648 015659 949611 908777 116970 749781 976794 902639 349577 490383 512913 753873 923396 786328 976866 620131 847244 818493 958556 622769 328138 859989 841407 187022 312076 846658 385762 739092 393261 635908 331280 454687 104223 264534 108591 885194 917665 257181 994963 130729 771285 533535 659376 436760 508953 105603 200284 099901 959900 503394 761872 584601 435738 912430 893137 942212 286902 464500 859553 876169 817634 445062 425478 330188 569095 229114 512176 333830 984251 784253 850758 364579 038594 101202 484422 527146 119459 758934 267697 467126 699538 002386 074719 291861 534119 282800 089260 201258 668485 491228 295398 040188 864522 527629 561789 666152 650601 463924 841780 567944 562221 734135 122918 333360 151754 014261 367073 256237 313884 783699 532905 850409 819987 437483 262609 567146 219718 949282 474666 454572 693984 403484 009044 009577 410803 476869 016227 951843 174729 531198 850067 075800 956791 640889 340316 463861 246088 972232 570764 643541 278624 870816 768769 908744 846158 205214 484034 689797 713527 079288 516960 022253 652870 079485 299968 503796 472324 554752 / 901 > 42889 [i]
- extracting embedded OOA [i] would yield OOA(42889, 579, S4, 5, 2702), but