Best Known (240, ∞, s)-Nets in Base 3
(240, ∞, 113)-Net over F3 — Constructive and digital
Digital (240, m, 113)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (240, 112)-sequence over F3, using
- base reduction for sequences [i] based on digital (64, 112)-sequence over F9, using
- s-reduction based on digital (64, 164)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- T4 from the second tower of function fields by GarcÃa and Stichtenoth over F9 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 64 and N(F) ≥ 165, using
- s-reduction based on digital (64, 164)-sequence over F9, using
- base reduction for sequences [i] based on digital (64, 112)-sequence over F9, using
(240, ∞, 163)-Net over F3 — Digital
Digital (240, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (240, 162)-sequence over F3, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 151 and N(F) ≥ 163, using
- t-expansion [i] based on digital (151, 162)-sequence over F3, using
(240, ∞, 495)-Net in Base 3 — Upper bound on s
There is no (240, m, 496)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (240, 2968, 496)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32968, 496, S3, 6, 2728), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5398 481205 887330 361121 894774 225042 294068 516746 380905 187787 778148 151242 808067 063957 811392 530789 678339 853436 178763 742424 425898 938111 462418 435616 525381 852523 816568 874840 520072 034445 502003 871927 692514 763717 353064 404670 413281 811455 085507 886476 786300 834886 117379 040757 996803 117299 097317 751560 166576 049360 684648 381881 427934 036543 134936 533998 797995 103520 833062 126937 477897 394439 890763 901490 793173 675122 915995 285984 100426 292609 250744 074122 140743 204291 759711 917365 427849 548013 190300 952311 758266 809395 577106 261330 318369 193861 258210 466553 545542 844783 610348 007718 046260 886728 092895 580161 231003 453678 274239 068781 557045 871831 000125 455763 130861 669157 122736 738535 239197 753910 616126 145848 634812 342208 416430 345447 209243 069559 002755 030443 932560 345069 895959 375517 125441 596848 567222 153168 276811 051150 689092 795888 015663 734437 580459 718875 001228 331706 856837 337225 959578 892688 808389 226650 876753 828925 113198 165827 017458 071302 637382 552072 501208 015145 858317 373838 853439 326444 624304 533140 562746 237049 922361 147103 887403 589503 451523 235029 565776 867654 042792 303193 146777 585067 223809 352736 826881 139337 820473 636329 376226 528532 439414 407015 176660 284855 532972 328504 015678 125673 369098 613583 025313 768914 744256 963533 742904 598362 330576 110807 887094 188783 285253 443601 021121 203061 925667 424622 616849 461745 681659 884394 617249 815110 553982 823537 415394 133089 235765 011730 020520 093517 416560 631598 225918 057129 606074 938133 075158 742520 746633 084218 680681 622403 969842 508310 215369 / 2729 > 32968 [i]
- extracting embedded OOA [i] would yield OOA(32968, 496, S3, 6, 2728), but