Best Known (9, 9+∞, s)-Nets in Base 64
(9, 9+∞, 177)-Net over F64 — Constructive and digital
Digital (9, m, 177)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (9, 176)-sequence over F64, using
- t-expansion [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- t-expansion [i] based on digital (7, 176)-sequence over F64, using
(9, 9+∞, 209)-Net over F64 — Digital
Digital (9, m, 209)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (9, 208)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 9 and N(F) ≥ 209, using
(9, 9+∞, 650)-Net in Base 64 — Upper bound on s
There is no (9, m, 651)-net in base 64 for arbitrarily large m, because
- m-reduction [i] would yield (9, 649, 651)-net in base 64, but
- extracting embedded OOA [i] would yield OA(64649, 651, S64, 640), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 114386 764185 097469 509594 013011 083728 379992 475043 378107 764625 002247 586091 995686 169225 781700 506223 098133 079821 017972 779359 891147 299210 106954 727118 694686 457079 711909 153618 371788 750722 861556 532580 906579 707004 991125 790021 579203 052705 806478 934320 014127 758140 958486 208044 094405 351305 891551 987922 912610 677140 621280 464443 313646 310417 730594 586501 433013 698910 190018 741389 192456 803038 240194 886948 672905 561204 070376 097810 035707 324346 256972 892135 165090 150367 270162 615828 260579 389953 630004 303295 436931 454503 168470 555870 815811 378255 914851 202810 713016 836139 948821 887425 185396 396758 185588 348450 663368 660520 828362 412858 227510 653287 979840 261328 105869 149089 102379 333703 090265 374026 864295 354267 449787 722465 986772 594894 898290 280475 342978 966714 635604 320001 455409 746076 681946 979597 900776 456400 317509 754317 138889 471671 315428 407719 560571 170226 631213 968640 473211 450584 478289 344230 080730 917082 222616 521280 433737 654476 417797 244194 607748 024812 604642 217397 134648 488812 726111 682228 586264 033451 353303 152405 606890 894806 172275 410656 499299 821138 547680 053377 374198 803259 555037 937972 218931 368109 841433 639703 988528 247989 162690 858593 224135 098890 127296 965739 758344 457781 337628 992307 073808 062950 205969 135953 034279 387136 / 641 > 64649 [i]
- extracting embedded OOA [i] would yield OA(64649, 651, S64, 640), but