Best Known (94, 94+∞, s)-Nets in Base 9
(94, 94+∞, 222)-Net over F9 — Constructive and digital
Digital (94, m, 222)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (94, 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
(94, 94+∞, 245)-Net over F9 — Digital
Digital (94, m, 245)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (94, 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
(94, 94+∞, 779)-Net in Base 9 — Upper bound on s
There is no (94, m, 780)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (94, 2336, 780)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(92336, 780, S9, 3, 2242), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 099244 370833 807733 222066 540084 911132 456865 296633 972396 317434 760524 350274 474835 148146 872738 343552 285047 308453 262296 789054 270756 624012 885972 265761 560493 051501 345163 911500 465095 913426 739376 169714 016474 240449 684627 689078 434488 255434 680895 538252 516248 402076 181190 259892 389531 020756 625885 322464 751696 520770 265149 219424 597324 290647 795556 217382 179151 127046 057648 956823 998274 353914 118827 759758 187453 434381 620696 673505 010268 013700 311223 168745 964405 306129 452229 813126 681796 890733 020973 382505 153618 318676 684358 499880 884992 308635 550817 099234 500736 411023 826860 558827 641199 277052 496293 315726 720723 211503 409424 020478 591997 415906 317365 075797 104068 871065 022022 126427 243445 812446 214711 619230 336422 452107 940026 055673 835315 061160 348805 437662 060856 813007 985243 475956 292129 489645 327712 037690 567202 667479 317793 356936 118357 928394 622886 284139 713143 671813 013166 267615 019705 563136 080778 098059 416839 852353 791387 265217 642539 098138 328810 948923 933141 073410 156169 234346 402219 061443 898493 433178 609819 118203 331770 820578 621387 617435 259362 655003 241354 774107 736821 148001 317685 418693 138412 202617 260447 780419 495718 458677 892612 342757 662707 018277 810229 349941 223585 352359 525455 913604 152098 287956 403301 100845 108293 593727 908933 898132 984141 448986 864331 726447 438245 421928 610194 056981 719231 830331 317438 803341 689439 756281 661826 777957 807484 700748 205174 676258 267764 453727 017479 384204 066109 717358 346799 705534 095407 100093 356964 617034 848634 751511 944217 464971 764373 245993 969215 329598 546096 014789 515836 518999 740587 124988 118042 654600 757462 436884 530070 131095 589652 139724 430960 954287 327460 625818 180440 569875 653859 171305 301014 737417 763956 929136 587415 222678 887190 016691 731061 081418 007031 001450 034090 678036 302635 251073 343927 597478 472602 262545 431427 224783 718152 209041 897850 456238 685580 841162 301572 630939 689427 668338 422678 051548 338443 765536 348252 818812 529951 999206 061131 544576 397391 286563 422657 040014 229210 875358 059764 001593 243350 163624 854200 390886 931708 822717 411383 215353 169402 090790 270001 006500 633970 177025 135044 143313 939531 415048 668786 696659 226114 119629 483807 219346 140319 003230 252925 769474 638696 280127 105566 811338 684816 463382 555074 454714 288040 767862 833871 470582 838544 529490 295542 925944 189706 658761 058263 361703 265417 637122 114895 129771 639970 172021 912278 272312 947907 382399 697214 615896 840132 532323 / 2243 > 92336 [i]
- extracting embedded OOA [i] would yield OOA(92336, 780, S9, 3, 2242), but