Best Known (61, ∞, s)-Nets in Base 7
(61, ∞, 54)-Net over F7 — Constructive and digital
Digital (61, m, 54)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (61, 53)-sequence over F7, using
- base reduction for sequences [i] based on digital (4, 53)-sequence over F49, using
(61, ∞, 105)-Net over F7 — Digital
Digital (61, m, 105)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (61, 104)-sequence over F7, using
- t-expansion [i] based on digital (43, 104)-sequence over F7, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F7 with g(F) = 43 and N(F) ≥ 105, using
- t-expansion [i] based on digital (43, 104)-sequence over F7, using
(61, ∞, 387)-Net in Base 7 — Upper bound on s
There is no (61, m, 388)-net in base 7 for arbitrarily large m, because
- m-reduction [i] would yield (61, 1160, 388)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(71160, 388, S7, 3, 1099), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 59102 834997 608760 147074 453409 908990 070541 066786 245708 792866 162425 046347 829171 216540 622224 091064 362220 142896 752986 967018 979475 266917 757863 456252 407254 419334 228912 441312 754817 903319 537877 239122 658359 868516 388212 888014 674034 761627 342158 507861 858036 486677 726037 614771 918564 552000 282440 373759 664936 083908 378069 575930 794822 881061 753225 224532 051701 694919 803905 021262 719732 161747 099839 239466 106227 142459 604806 388095 506461 080969 503913 030315 953202 901650 333319 694082 884567 403778 641369 380605 109819 222976 118002 156135 432884 674224 860823 655067 532105 644409 457780 822116 200028 840526 649777 589993 526538 077356 304203 080046 253281 017185 406059 543664 420256 872025 335481 792370 681392 608416 917732 095320 831027 857811 257257 761444 752519 056385 296816 771326 364640 007480 426854 968051 346219 637149 861675 159638 727078 934770 624351 961377 842192 404764 481559 539495 954943 984335 890734 648166 129685 916932 413577 363951 499807 928061 175483 479312 872793 314019 195588 100333 098842 234315 955262 247403 094152 685251 433182 577033 639558 411989 207633 352287 / 275 > 71160 [i]
- extracting embedded OOA [i] would yield OOA(71160, 388, S7, 3, 1099), but