Best Known (250, 250+∞, s)-Nets in Base 3
(250, 250+∞, 123)-Net over F3 — Constructive and digital
Digital (250, m, 123)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (250, 122)-sequence over F3, using
- base reduction for sequences [i] based on digital (64, 122)-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, 122)-sequence over F9, using
(250, 250+∞, 163)-Net over F3 — Digital
Digital (250, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (250, 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
(250, 250+∞, 515)-Net in Base 3 — Upper bound on s
There is no (250, m, 516)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (250, 3088, 516)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(33088, 516, S3, 6, 2838), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 9 499439 712768 522985 315227 186954 586536 566072 733195 044709 530441 947733 512972 246851 800510 141670 839586 770808 011634 606611 789601 472100 628116 577073 492553 290991 962240 944143 429634 009320 011973 965392 545733 654955 362540 497589 769039 134147 563665 383609 196014 308556 611212 601247 600629 729184 551968 457115 586583 180406 223240 662040 815471 091194 606078 546447 152354 097614 678583 062636 453244 074449 855757 113628 121504 026627 587356 952299 190566 803919 751400 087044 613092 907014 341751 713323 869451 938056 094748 525174 619308 078372 041854 216737 547267 533021 504922 224491 331730 397943 697273 290783 834133 579732 056182 276906 013108 612932 263301 641815 878475 948231 540788 822196 135546 464977 544047 668753 293276 910511 949358 663952 246507 294430 482959 391938 400988 742441 968516 822668 595949 211731 294360 028624 711240 959593 474019 061736 877609 116649 817556 350581 876831 651057 153615 154818 891155 236973 885680 246153 140312 016278 530517 378001 599144 181251 673072 514920 495504 574409 713659 260801 403699 145561 269811 519461 680264 797983 348763 354923 330036 943795 206275 436924 968904 442870 641971 289006 027792 504901 752213 700320 296142 788504 081190 599723 811461 196027 060057 005109 746572 936425 127929 152512 638107 048319 703476 127617 820969 577450 576265 446033 117220 010718 560460 592246 812093 250627 742419 159141 646907 402734 862284 703835 912629 640938 677676 225532 576664 272051 077695 703174 993701 207249 560220 970028 377685 875698 789718 329653 003607 801895 693778 748717 072362 993558 615812 064403 222994 318724 234369 483951 042895 958287 440972 070304 179171 498873 570765 296111 684104 873115 204861 741177 374423 545430 662479 / 2839 > 33088 [i]
- extracting embedded OOA [i] would yield OOA(33088, 516, S3, 6, 2838), but