Best Known (103, ∞, s)-Nets in Base 9
(103, ∞, 222)-Net over F9 — Constructive and digital
Digital (103, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (103, 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
(103, ∞, 275)-Net over F9 — Digital
Digital (103, m, 275)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (103, 274)-sequence over F9, using
- t-expansion [i] based on digital (101, 274)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 101 and N(F) ≥ 275, using
- t-expansion [i] based on digital (101, 274)-sequence over F9, using
(103, ∞, 852)-Net in Base 9 — Upper bound on s
There is no (103, m, 853)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (103, 2555, 853)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92555, 853, S9, 3, 2452), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 386081 999600 375703 760298 318011 594888 145060 427441 743611 456275 824041 008881 333876 655466 752566 950295 632687 170064 349876 882212 575868 734566 674904 476167 550423 233305 537104 321415 090349 967001 029853 162311 901573 797133 254538 464764 169253 870166 700716 790490 869507 733360 675606 511774 650766 861086 514074 111750 904587 535743 323280 838720 928670 132736 591749 616326 891891 103605 605784 161650 219698 587609 181204 542404 168943 056985 701234 613052 179570 959309 587638 940167 271843 945876 205585 752020 562683 574331 533432 442730 725733 043016 041451 970769 081073 317892 502589 733808 076479 917832 233963 900039 512491 401319 291146 932482 757831 615123 778921 326076 945589 167713 394722 653681 199662 094451 076611 847656 599096 057957 569613 187689 111899 093069 132636 731051 711886 546994 751495 678307 381856 466655 257773 711132 499000 418747 068782 500678 673054 210385 871703 320128 287298 613885 875550 297659 806521 403792 675064 356649 061029 969563 262682 327584 071957 964520 545122 388605 582504 001723 986265 591210 134667 011338 819659 010525 951822 337693 543389 417160 511805 384114 705312 664402 235664 932730 130027 829103 728500 207158 149642 668334 032929 313051 057115 668193 273863 933720 860688 868532 889847 536266 832786 157009 671435 428093 988468 755583 978359 606838 799754 712065 724933 233827 611303 151382 532078 518699 065004 575789 856294 677548 045082 002679 739162 030465 805710 005516 038268 643206 390817 786775 231964 779108 598337 735359 218675 820678 331901 200138 744251 510816 580447 541722 844230 918454 185684 455676 067950 002838 726569 266076 171785 927233 088281 242903 736618 299849 007571 968315 564549 396353 858847 679427 828352 068127 157997 859091 757554 559972 157983 894840 953898 447759 091877 462477 330514 155276 543780 856479 567474 125808 933650 128679 437772 188319 068308 125720 842871 429687 493320 502951 676953 068715 784504 889004 526115 987148 078592 079488 198124 472315 618643 181204 484388 790804 713369 430143 839411 053920 395488 136743 075661 408294 448801 330796 228022 282268 929232 682653 816722 214027 403805 351842 438587 833100 574482 523497 149310 039649 110916 087332 266728 710200 040899 870703 246313 063871 502440 220388 122485 764612 387256 518058 050414 989833 213508 108403 860569 031261 942979 745591 063244 160337 357527 656590 390479 470739 990151 671679 191123 427944 314716 703429 171708 461607 069365 996352 129905 392421 042748 877526 983227 999938 151753 263739 014837 939980 088018 529689 045054 815169 056926 215233 746960 324185 871536 110081 578909 406847 032024 317250 448821 485068 061546 020997 873711 599588 772800 790518 376613 848943 824255 687097 157440 754445 939831 332705 045543 555709 224544 307023 413157 203990 152483 327033 691143 891262 453872 389769 858706 064298 036527 751218 784118 386281 870909 / 2453 > 92555 [i]
- extracting embedded OOA [i] would yield OOA(92555, 853, S9, 3, 2452), but