Best Known (76, 76+∞, s)-Nets in Base 9
(76, 76+∞, 165)-Net over F9 — Constructive and digital
Digital (76, m, 165)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (76, 164)-sequence over F9, using
- t-expansion [i] based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second 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) = 64 and N(F) ≥ 165, using
- t-expansion [i] based on digital (64, 164)-sequence over F9, using
(76, 76+∞, 192)-Net over F9 — Digital
Digital (76, m, 192)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (76, 191)-sequence over F9, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 61 and N(F) ≥ 192, using
- t-expansion [i] based on digital (61, 191)-sequence over F9, using
(76, 76+∞, 635)-Net in Base 9 — Upper bound on s
There is no (76, m, 636)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (76, 1904, 636)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91904, 636, S9, 3, 1828), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 193 564335 921552 625658 366773 591142 987175 476009 912637 548931 014635 606312 806156 615313 072527 963040 399211 261987 173757 574115 010708 228142 627286 347407 792961 252738 381719 683033 620074 121215 802091 934433 957984 826520 946774 292647 636828 089342 224534 999668 157697 074591 954631 339914 745663 262065 689197 572960 448011 727519 461616 410133 084331 153007 590817 476892 355382 023330 471734 510067 250298 632106 403829 123124 320604 049570 613135 890548 362899 203549 629040 092531 128155 235021 949508 819051 985607 847233 629514 261416 716944 863334 894067 775693 839957 084633 995739 384595 593526 978582 395689 881987 298085 878792 814849 164173 467441 837500 267293 403151 096533 521747 627137 012854 641454 666637 487435 037985 689975 501072 188625 444320 447477 388338 092488 386435 050293 322300 706853 761615 409208 825867 464069 889919 538229 731910 381923 426808 342467 297775 476344 225955 801125 266411 358821 762780 647627 283675 016699 814767 759234 938079 147960 005327 928567 870433 103652 760704 547061 960601 733003 306516 689896 777842 365761 502420 795449 800038 059905 399810 264653 689174 025620 186709 121298 183218 367036 526773 106128 837811 668516 753487 044917 042983 649900 150041 271828 036290 490472 900538 708627 186663 893457 257981 341598 485248 776328 121795 099179 941658 125616 248873 312157 212167 566822 226013 114549 527622 619442 227743 983751 085457 325342 442531 176554 563304 398024 547161 374141 110502 453024 565800 885513 419647 815404 774057 404397 383330 761850 507877 247747 584131 720074 473925 027750 730700 878768 174508 101143 835814 976361 719549 003177 062240 169452 198162 889904 372985 791437 653608 019741 335367 724472 916052 212885 801912 610796 312628 061443 980672 406456 898702 194523 279446 790961 055066 247921 132954 615911 949038 400860 836052 147839 050091 258026 813771 975377 982384 798161 093257 884017 263456 272052 639937 651145 670395 191553 346954 960483 305020 226480 593900 958156 555338 094450 505118 068195 517231 954932 222540 420392 367329 030700 797701 764927 115514 759707 095347 109292 484451 944689 296650 350236 568965 / 1829 > 91904 [i]
- extracting embedded OOA [i] would yield OOA(91904, 636, S9, 3, 1828), but