Best Known (10, 10+∞, s)-Nets in Base 64
(10, 10+∞, 177)-Net over F64 — Constructive and digital
Digital (10, m, 177)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (10, 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
(10, 10+∞, 225)-Net over F64 — Digital
Digital (10, m, 225)-net over F64 for arbitrarily large m, using
- net from sequence [i] based on digital (10, 224)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 10 and N(F) ≥ 225, using
(10, 10+∞, 715)-Net in Base 64 — Upper bound on s
There is no (10, m, 716)-net in base 64 for arbitrarily large m, because
- m-reduction [i] would yield (10, 714, 716)-net in base 64, but
- extracting embedded OOA [i] would yield OA(64714, 716, S64, 704), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 104 891764 158992 863071 693496 975264 067254 757454 054379 105262 957423 160867 329675 959264 186313 518205 802838 511358 198454 397643 208209 628016 661324 408983 539182 920478 096991 751922 816493 686674 723660 395159 796804 202453 769671 348318 667752 077683 644505 897972 243194 104454 383660 539587 592661 512909 522658 342421 146502 925106 604274 925604 737137 831770 453668 116209 794384 448553 319347 998868 850802 644118 797513 002559 538458 779475 129707 755090 357256 353451 752557 404031 421270 364666 170725 403485 104701 782569 972328 691649 432865 234316 666312 029966 846097 927058 512541 543030 735139 514942 452730 296817 992409 448522 996998 669701 829936 490120 049828 424385 270787 870231 647742 711180 833664 921004 704408 823781 280515 597385 500403 114766 613417 151920 595723 174733 146634 951640 037612 899819 017853 628543 905791 125945 234931 745136 946085 245995 607283 533611 912631 255222 486593 676395 684866 757188 801970 151146 350424 396366 653119 399435 199013 249582 001087 790040 463805 926057 031240 260890 239747 826267 430811 070618 514436 365038 354583 693357 966243 033713 199969 974073 218040 209445 838235 131328 182751 679464 924282 159987 055890 958862 109166 197989 265192 082806 058460 635794 217986 703622 086053 255309 500093 062210 920932 954709 763571 373768 075947 033570 368059 725173 994648 850412 948133 214096 223251 873108 234172 967733 522234 883281 397750 191910 820591 196910 409483 263660 545053 956494 573336 682534 698048 002536 752489 168896 / 235 > 64714 [i]
- extracting embedded OOA [i] would yield OA(64714, 716, S64, 704), but