Best Known (164, ∞, s)-Nets in Base 4
(164, ∞, 200)-Net over F4 — Constructive and digital
Digital (164, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (164, 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
(164, ∞, 215)-Net over F4 — Digital
Digital (164, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (164, 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
(164, ∞, 509)-Net in Base 4 — Upper bound on s
There is no (164, m, 510)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (164, 2544, 510)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42544, 510, S4, 5, 2380), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 149326 126724 061166 089158 143856 728602 033377 986753 139823 338889 892342 194183 387216 626655 333003 312020 604308 893492 558638 487220 635094 872507 427227 109034 755835 163283 693099 978661 137388 373134 192355 812405 078583 937898 653633 321687 538465 582216 790065 173944 140094 543512 405202 943429 936136 147375 031039 762852 926269 992918 970060 771354 462117 694717 725457 557467 071712 135228 973288 787723 067564 356767 225663 713731 698775 587783 149123 746424 633236 403216 294519 380401 064995 973783 184157 741213 720490 333171 833853 371444 847554 583404 526546 956609 075394 171879 390365 426239 477373 309252 940273 618252 293973 788126 246771 079217 157238 911044 526724 177981 522492 834003 414183 016523 707435 238363 127380 285016 254764 874978 415356 675523 335219 422375 793818 325237 855873 253850 964029 830314 949211 910702 807438 203056 888131 625810 741844 425624 537628 305599 151732 160074 289781 288303 744197 275912 623980 698479 920677 102644 014330 534655 955712 341062 772464 946913 073284 447122 055726 588758 131489 684816 535528 666217 313769 083329 517675 512772 490674 205493 321343 756179 696555 667274 417981 500339 171364 303004 061576 010695 013306 798451 065605 759694 670332 873503 756031 438798 388509 239572 251991 536825 550178 468658 839018 213726 074316 257731 091436 629144 074320 346530 957937 992914 011768 452318 298193 584075 218265 259778 101442 494239 646470 026074 065424 265119 790424 076869 068966 603925 812357 054507 393944 030841 015512 460073 342192 234016 770525 028692 917929 220174 675490 340566 616532 821104 790514 775259 691223 713465 049834 669103 987969 705800 328895 011786 353347 193060 636450 118026 541796 125551 687837 582729 847926 995261 892816 134389 248039 982838 033368 053002 377601 968571 861272 887296 / 2381 > 42544 [i]
- extracting embedded OOA [i] would yield OOA(42544, 510, S4, 5, 2380), but