Best Known (63, ∞, s)-Nets in Base 9
(63, ∞, 81)-Net over F9 — Constructive and digital
Digital (63, m, 81)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (63, 80)-sequence over F9, using
- t-expansion [i] based on digital (32, 80)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- F4 from the tower of function fields by Bezerra and GarcÃa over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 32 and N(F) ≥ 81, using
- t-expansion [i] based on digital (32, 80)-sequence over F9, using
(63, ∞, 192)-Net over F9 — Digital
Digital (63, m, 192)-net over F9 for arbitrarily large m, using
- net from sequence [i] based on digital (63, 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
(63, ∞, 530)-Net in Base 9 — Upper bound on s
There is no (63, m, 531)-net in base 9 for arbitrarily large m, because
- m-reduction [i] would yield (63, 1589, 531)-net in base 9, but
- extracting embedded OOA [i] would yield OOA(91589, 531, S9, 3, 1526), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 12 146162 839469 129009 559311 526327 436890 634485 737593 594484 474027 044904 153796 389168 304395 468203 965624 546634 691457 647754 015676 778643 822628 805053 070147 836567 686969 133875 943488 739086 139864 604429 309222 729064 071967 367126 139277 160362 074970 706291 756577 724003 431886 824053 139358 200111 152115 162500 358751 384918 446240 440283 974346 080348 153818 365263 612209 175710 467901 858973 367130 918485 078921 116197 849493 769912 601577 372919 488836 480765 033978 958905 294585 607604 335391 422141 718057 638394 165441 026953 665702 919874 694130 105033 653485 495968 969100 134572 022237 340232 343412 560306 264655 713797 272072 483101 200867 750377 696799 668313 638394 408461 669799 126972 777477 190573 651938 513742 821669 452627 804191 496882 759808 059204 925672 474171 999332 001051 719805 323369 851279 519314 926312 815365 804620 868662 335990 621779 839229 598071 104589 848938 915774 013797 210668 249893 994042 498270 141836 969409 656077 684724 051558 470946 532854 095316 049090 908539 171948 431726 920858 514482 275097 487686 476354 404292 458405 797277 602653 615782 784130 696522 341741 811048 886872 918187 159412 086400 019459 668352 182067 050365 889985 596170 631736 367978 875680 914948 092530 950861 023660 318242 292186 243522 522303 210385 974067 532430 150880 505450 309303 507130 478522 768691 038549 163102 514691 590235 544939 046903 729442 260050 431308 882986 591817 319569 227880 688820 380628 385044 369211 577323 867101 925805 110017 523318 026977 870845 947899 221257 554267 498434 094685 984729 107955 041211 782598 103171 133148 660068 587534 393078 467379 542275 339983 020439 337833 619018 417673 992728 165544 691517 925762 295797 112399 405019 705332 975536 369450 523775 202065 423015 788037 892469 / 509 > 91589 [i]
- extracting embedded OOA [i] would yield OOA(91589, 531, S9, 3, 1526), but