Best Known (86, 86+∞, s)-Nets in Base 9
(86, 86+∞, 222)-Net over F9 — Constructive and digital
Digital (86, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (86, 221)-sequence over F9, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- F4 from the tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 79 and N(F) ≥ 222, using
- t-expansion [i] based on digital (79, 221)-sequence over F9, using
(86, 86+∞, 245)-Net over F9 — Digital
Digital (86, m, 245)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (86, 244)-sequence over F9, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 81 and N(F) ≥ 245, using
- t-expansion [i] based on digital (81, 244)-sequence over F9, using
(86, 86+∞, 715)-Net in Base 9 — Upper bound on s
There is no (86, m, 716)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (86, 2144, 716)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92144, 716, S9, 3, 2058), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1947 670297 419393 204638 677694 218763 223257 151854 277332 763871 357874 520060 344447 839115 140989 617129 404841 799475 752030 987442 525551 922603 897502 402032 175485 743158 068329 216554 646525 096680 389083 963203 188908 405704 318689 807844 128175 631887 427250 685082 898595 055432 013337 210639 366866 921421 604176 203158 504280 491607 836001 324963 479413 840235 237151 982879 104530 365831 243279 269807 106020 074704 617871 315261 984900 985488 153242 451726 077148 998724 151327 195861 016603 319329 483424 681565 104490 079403 990072 308393 735689 997681 293631 019153 832534 249478 339756 385091 874462 331155 367480 809177 328465 483523 510157 809487 178057 424458 089970 531241 213395 447231 724664 595837 541824 434250 393871 746445 855156 752614 241011 722384 838375 399835 408605 792131 159252 239047 409508 613603 783634 334138 625422 381086 622729 498131 378743 191960 480601 617061 754972 205613 751785 503559 853595 837968 295670 266251 956285 574262 032345 748045 083470 316438 985984 837518 125141 307775 993515 447545 664994 590687 545876 269492 950559 705850 880599 733545 272253 391039 743743 159102 033549 432076 801432 918427 997801 648250 348828 765528 349284 404613 943043 381153 129158 920355 475282 939412 263591 352814 100431 455482 655874 228139 422953 849275 111889 297508 020395 640227 939632 612179 704535 355659 254881 257966 460684 991227 075773 930282 331369 546364 430094 498836 894227 723534 221156 453798 702418 318455 170986 255481 920974 457193 977174 831267 177191 333293 890419 057775 380325 278957 882266 740666 285963 096138 287076 123294 813862 395688 218118 737224 228381 327482 842375 873763 974254 111902 505738 957971 659009 346913 876039 664652 571944 107194 202359 786706 830602 384995 004709 255376 783736 430114 579782 539941 732545 999645 590377 165869 851296 463796 910075 358246 531950 275550 978937 415179 849385 608053 725563 637969 354493 475174 268276 348026 132367 222250 303640 805546 467976 316134 860037 161359 578864 459273 731579 002202 249529 690841 346027 552651 554165 030302 506923 702546 844761 566683 065604 499845 548642 099551 690613 594800 536918 339754 191964 808545 834871 638624 584880 522805 023694 360637 981218 225817 787709 323363 073704 913834 996604 504899 033144 690083 907116 860837 707712 283881 076285 937844 966568 902226 323773 877337 664355 042979 316458 799433 341283 606723 161227 298475 / 2059 > 92144 [i]
- extracting embedded OOA [i] would yield OOA(92144, 716, S9, 3, 2058), but