Best Known (96, 96+∞, s)-Nets in Base 9
(96, 96+∞, 222)-Net over F9 — Constructive and digital
Digital (96, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (96, 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
(96, 96+∞, 272)-Net over F9 — Digital
Digital (96, m, 272)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (96, 271)-sequence over F9, using
- t-expansion [i] based on digital (95, 271)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 95 and N(F) ≥ 272, using
- t-expansion [i] based on digital (95, 271)-sequence over F9, using
(96, 96+∞, 795)-Net in Base 9 — Upper bound on s
There is no (96, m, 796)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (96, 2384, 796)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92384, 796, S9, 3, 2288), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 6523 935099 574406 869247 132889 547627 255135 165833 059345 592502 298843 920810 648043 922134 164997 995666 883476 771575 521843 745383 535096 533707 597086 438687 462231 428760 931738 908393 246488 211247 210025 144182 479669 386120 300770 731953 282318 285982 214106 527230 574875 195664 548970 225759 771592 542161 905575 929279 334368 801894 834100 208084 784439 518409 843636 432454 579404 023143 725780 564488 962729 573984 633841 199649 095225 896358 381582 584206 318460 740201 453135 655212 389885 588817 432160 135219 356310 400640 598478 639442 582474 227311 797713 679950 992771 562206 501400 645164 303208 850035 645270 262343 243517 683877 995715 601971 698207 741804 292494 629236 434803 602485 606810 150130 597536 046376 107343 481086 293356 397065 211873 802252 965533 554061 519776 729901 817289 609194 490679 967177 641790 990087 199653 538397 751155 720431 207840 821466 934128 225979 215343 465595 947076 480116 644201 381494 133115 006495 616770 388736 102844 208898 833130 919789 456036 543146 815366 802321 308823 588359 102219 774825 248287 500309 946250 301660 851545 426395 983702 843234 072902 898651 308242 324234 946352 279596 408230 177228 365485 793591 096855 366066 342106 467486 288340 677818 110260 103810 554604 266039 880884 711507 696034 756646 349275 977003 520222 394422 465733 948584 070383 304892 617056 783857 497344 947736 584558 068083 551734 103680 217500 921068 023443 537082 929349 149681 444051 217074 365189 492167 362581 856735 957417 948185 770306 519987 267280 885640 793527 323769 395936 398559 770268 184323 637674 693494 661815 126481 666307 920708 797213 556064 763685 830307 491829 497239 403747 821549 395120 111642 628491 550286 059414 973373 638027 894574 191345 783719 171495 505051 481284 874400 348251 800399 523999 086386 207604 404395 874997 810803 155599 441632 871503 904719 064296 733319 811566 641041 544104 793269 346395 533715 525304 467690 725460 722100 222575 369311 278940 263698 247546 442564 027504 971145 126392 135324 160508 156720 097077 119214 712188 289688 223326 067115 127713 268017 623418 881061 637579 983653 814182 493325 648360 619230 002054 393836 526318 417672 517452 423438 080544 304510 343300 846284 343967 389107 642012 040272 363101 202696 780628 270841 496025 974985 698275 408772 852463 582751 902636 756140 073332 144691 765931 535271 501428 009699 550841 023026 506339 751388 478953 897814 533404 531882 599054 012144 414645 006321 691245 576557 900945 799925 290061 549630 662014 328126 563734 200358 827621 195567 866770 693091 577721 632712 551533 700605 164681 160754 745230 243321 427354 863922 037096 050298 130671 330550 582749 548857 000316 579995 / 763 > 92384 [i]
- extracting embedded OOA [i] would yield OOA(92384, 796, S9, 3, 2288), but