Best Known (167, ∞, s)-Nets in Base 4
(167, ∞, 200)-Net over F4 — Constructive and digital
Digital (167, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (167, 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
(167, ∞, 215)-Net over F4 — Digital
Digital (167, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (167, 214)-sequence over F4, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
(167, ∞, 518)-Net in Base 4 — Upper bound on s
There is no (167, m, 519)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (167, 2589, 519)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42589, 519, S4, 5, 2422), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 184 207411 354605 829323 270592 428328 987605 468721 024747 607475 246806 367612 097687 622885 255574 186811 597954 925781 973293 264882 474229 953446 658271 114693 177247 544733 588897 405857 703494 364110 659236 101158 761045 165182 270589 852374 430701 750447 340358 285969 940625 722650 095715 464072 917050 332036 115526 897882 719841 730103 767506 765973 950430 623238 939386 313522 241679 323273 502865 654531 498996 750125 684673 338725 830831 635991 009196 942162 889369 635657 142468 610516 175294 796058 052040 230126 968375 017773 117725 699511 493943 584902 075057 876848 252681 069363 954450 214269 651698 221721 492700 465378 891373 093595 717711 366888 629756 423801 164804 250059 708891 994911 933599 738552 974658 578796 711442 266893 020028 140679 091235 577464 445187 264096 113043 129073 409942 335593 018711 836404 969556 768186 667013 243949 518019 839389 170839 500069 774924 761260 736280 467054 382317 703474 742701 353685 515589 096680 569979 140589 986366 296260 389852 935745 607593 594082 497620 103708 894895 434216 111753 279653 641866 945506 077227 786499 176932 222421 049427 007185 848065 519497 141810 313543 977269 688713 275354 334590 047880 841658 084451 285558 264025 915829 430785 375255 229160 703078 954242 002255 893032 580994 603385 491125 696299 186689 116006 093946 332549 400231 056419 298401 951314 492553 460468 458116 685347 152941 040851 183565 045137 277006 330834 173765 320846 151992 255211 800005 921193 664562 040162 875202 780577 696216 221222 352354 811517 068973 616149 205510 343132 752381 553246 681709 286634 151948 104272 651417 227645 910519 205368 189531 893863 537614 479113 579134 240240 789368 418765 200773 664165 365019 177577 569078 981348 732660 203726 930364 452760 661613 364345 609106 797185 421995 400790 820573 678224 374821 014584 817170 251776 / 2423 > 42589 [i]
- extracting embedded OOA [i] would yield OOA(42589, 519, S4, 5, 2422), but