Best Known (7, 7+∞, s)-Nets in Base 128
(7, 7+∞, 216)-Net over F128 — Constructive and digital
Digital (7, m, 216)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (7, 215)-sequence over F128, using
- t-expansion [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- t-expansion [i] based on digital (5, 215)-sequence over F128, using
(7, 7+∞, 262)-Net over F128 — Digital
Digital (7, m, 262)-net over F128 for arbitrarily large m, using
- net from sequence [i] based on digital (7, 261)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 7 and N(F) ≥ 262, using
(7, 7+∞, 1032)-Net in Base 128 — Upper bound on s
There is no (7, m, 1033)-net in base 128 for arbitrarily large m, because
- m-reduction [i] would yield (7, 1031, 1033)-net in base 128, but
- extracting embedded OOA [i] would yield OA(1281031, 1033, S128, 1024), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3934 877223 864977 007084 515862 656895 606430 885916 043169 559197 025979 615463 111730 178630 983696 323230 921258 611118 134074 208959 789973 345058 623280 006355 308512 109110 515559 380498 261395 596498 110189 951388 056609 661200 048814 671769 667588 429038 864491 037324 857496 664503 721194 964804 626187 777240 888776 116083 376010 554358 486555 964379 928687 102374 654634 782872 097290 452890 190395 784467 993074 970331 844563 810853 990094 567528 126322 810269 920848 519092 107774 527003 733394 728580 989538 629662 558142 816492 173055 696158 081156 881048 581214 590252 458788 529245 877630 304250 064618 841263 013715 814559 344104 179562 694265 778820 278687 054383 856381 985854 985916 581916 683809 247888 572138 640804 330050 040265 897610 107452 966894 649976 027190 926701 102986 858960 118436 121830 116835 287695 899077 011632 118756 858904 110467 656406 551512 156654 817401 866569 304809 961527 566385 660570 047747 093284 932996 769458 765215 757807 087983 573807 015090 350085 216729 026488 411793 892304 365827 074098 961632 069479 143549 303583 957083 882568 299123 255114 696227 730313 313469 813070 395412 900885 567692 634379 305623 197349 698905 556934 033933 688418 108202 250102 283035 594673 595013 087184 289480 573560 660810 077042 312306 760306 482887 006271 151175 902025 683980 204616 481716 885630 123454 764559 597683 906305 777836 353219 463272 332954 362674 434897 840017 982835 226947 190370 044600 752891 590102 757948 260540 789236 129340 372817 342707 142422 010288 290615 248901 682116 838442 951055 167716 656221 449365 113492 803241 418840 012565 125141 737004 924091 272102 454151 735212 778119 490755 212176 463248 089108 737826 487295 464018 031760 874798 510142 675574 073541 674922 614163 362348 655637 432462 814174 141309 886574 123540 270566 774917 134661 629741 016478 964240 271600 139934 203947 439582 840314 096351 751290 386355 975859 194354 124414 913534 658444 333621 869687 980272 019793 120531 800461 221802 686357 867976 601305 505891 980864 364856 826312 024055 277692 162508 708774 012882 787002 207519 018626 075586 300291 060690 227950 830218 289967 777588 127365 165492 734017 556760 356979 510510 541184 874987 126514 306876 880322 836953 855509 969823 247829 322487 780832 346841 623667 073439 055832 962206 497896 849398 562264 878551 582600 618073 492068 253747 033026 345425 086286 900446 576901 107776 205666 637420 816026 530096 726368 266955 005947 625372 908224 054112 077110 667664 567504 201665 928361 090909 709992 812768 871576 788796 522515 922944 / 1025 > 1281031 [i]
- extracting embedded OOA [i] would yield OA(1281031, 1033, S128, 1024), but