Best Known (94, ∞, s)-Nets in Base 7
(94, ∞, 75)-Net over F7 — Constructive and digital
Digital (94, m, 75)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (94, 74)-sequence over F7, using
- Niederreiter–Xing sequence construction III based on function field F2/F7 with g(F2) = 21, N(F2) ≥ 2, and N(F2) + N2(F2) ≥ 75 from GarcÃa–Stichtenoth tower as constant field extension [i]
(94, ∞, 105)-Net over F7 — Digital
Digital (94, m, 105)-net over F7 for arbitrarily large m, using
- net from sequence [i] based on digital (94, 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
(94, ∞, 587)-Net in Base 7 — Upper bound on s
There is no (94, m, 588)-net in base 7 for arbitrarily large m, because
- m-reduction [i] would yield (94, 1760, 588)-net in base 7, but
- extracting embedded OOA [i] would yield OOA(71760, 588, S7, 3, 1666), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 404 403168 351003 428414 538108 774412 624032 999286 479667 196745 218083 096277 100303 805138 689200 456386 994375 199925 073785 408764 109242 331278 407618 676781 835430 409696 257813 904428 955372 287580 823536 330112 882534 023834 446647 528553 701904 643195 293855 253922 602644 885393 611065 580016 543437 568814 930673 386499 137223 370792 178407 116177 606293 879651 318939 412523 346875 767492 937345 087587 323980 501850 728194 008657 460942 292751 963483 157204 136388 643422 453816 808730 226992 873421 582607 900303 339294 147437 583740 789571 282348 226603 689044 160159 958776 067679 840923 810971 055139 584158 053900 362941 980828 530828 466275 412973 024001 509303 000014 040848 801628 630488 911157 624108 392100 687072 076523 997640 479369 129948 116193 774428 725294 361761 762642 795680 531393 784064 153277 631110 229411 376559 945391 741916 105537 208913 804434 260933 623727 685430 370272 261563 742751 492778 678553 709824 301385 456487 061603 237305 583569 059721 733827 400573 913319 774129 658099 262230 861250 154298 778270 330886 853374 996855 959626 593191 246554 769129 403258 391575 517733 252081 065789 088386 517689 490197 166932 479657 734267 908733 757827 592700 712560 732526 764358 683604 164201 806480 327996 608757 026814 669447 565862 771574 988117 884474 792013 269650 753282 317007 796575 142949 631505 047681 860763 119737 873387 247112 970453 367594 959690 632011 938758 768893 743432 662688 626049 908127 245475 853848 412637 144593 176767 868352 760836 864676 377649 691367 001253 286076 100855 485792 052671 820155 617039 367476 858946 871812 339224 724437 420181 545895 042938 748847 698827 449247 664986 959856 438791 132436 610757 976782 542139 008530 182933 692749 367567 766483 041715 / 1667 > 71760 [i]
- extracting embedded OOA [i] would yield OOA(71760, 588, S7, 3, 1666), but