Best Known (85, 85+∞, s)-Nets in Base 9
(85, 85+∞, 222)-Net over F9 — Constructive and digital
Digital (85, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (85, 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
(85, 85+∞, 245)-Net over F9 — Digital
Digital (85, m, 245)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (85, 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
(85, 85+∞, 707)-Net in Base 9 — Upper bound on s
There is no (85, m, 708)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (85, 2120, 708)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92120, 708, S9, 3, 2035), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6126 488343 540404 866766 541038 699947 992814 008265 257108 176035 808411 119303 900461 888847 910548 116313 747163 541839 140056 338221 649918 376701 196666 856116 409437 049511 654144 765822 676425 411338 994417 009128 002429 400722 128478 236996 270123 929175 010436 683732 693642 658117 834464 287957 373894 873919 605526 379484 421238 712935 855751 281541 124959 982768 767483 490796 704345 318113 720921 981680 637672 123963 880291 125568 672159 250428 294863 316204 746932 544588 610731 993021 646494 978879 454783 483509 756769 299219 815844 131715 172852 760234 930596 522151 253529 770256 596091 195970 977789 358290 246064 367100 779716 510151 575481 673652 225065 101769 545957 548815 690384 960097 555959 766618 042406 173224 882192 447819 070418 351710 402678 635765 374393 245349 468463 840497 617077 407989 012727 257820 815081 218253 421122 580773 963199 510810 722356 499790 880922 195643 785654 944828 913662 628010 936174 544315 628508 056962 723780 892470 326161 014613 972595 448531 437342 758173 911324 983127 428455 945323 325381 497338 443680 894524 476600 995160 312040 972536 693353 356410 547387 824315 551058 615225 959971 468056 596964 478717 607800 168244 304264 159493 713175 651882 744387 493373 673836 151332 236654 699112 191740 252249 533674 346903 415043 988895 141978 095787 485002 904762 073891 908229 121336 399448 632059 474196 289599 551785 194967 690529 007903 918630 636973 537754 180873 057146 276301 705790 568600 170547 885006 431473 828063 752220 991697 889476 326780 516185 173592 396122 053245 532678 752565 344798 919513 090051 641146 850901 832961 442450 287883 690316 759525 040975 145641 059071 223576 278849 690461 299861 973712 438664 502996 984188 411901 866373 191483 286402 684438 341107 569884 485136 815194 453501 633933 213797 802004 830220 323583 977183 478363 568102 689418 584380 420652 620491 725824 487975 464554 943778 426397 748359 419189 725530 519304 607206 741485 637582 923721 644918 906506 277098 650051 740159 640871 628129 702944 003489 915494 221621 874298 600439 630654 105834 545708 954411 038432 551112 877155 988795 700594 306043 245364 999757 882721 682900 109133 277312 480358 693548 865418 980236 743619 979935 460249 954198 212135 253586 482807 423734 494498 087991 335844 211990 999506 434636 406095 794332 408795 003425 233695 805782 265829 037588 880771 212721 988700 789421 / 509 > 92120 [i]
- extracting embedded OOA [i] would yield OOA(92120, 708, S9, 3, 2035), but