Best Known (223, 223+∞, s)-Nets in Base 3
(223, 223+∞, 112)-Net over F3 — Constructive and digital
Digital (223, m, 112)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (223, 111)-sequence over F3, using
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on function field F4/F3 with g(F4) = 79, N(F4) ≥ 2, and N(F4) + N2(F4) ≥ 112 from GarcÃa–Stichtenoth tower as constant field extension [i]
- t-expansion [i] based on digital (189, 111)-sequence over F3, using
(223, 223+∞, 163)-Net over F3 — Digital
Digital (223, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (223, 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
(223, 223+∞, 460)-Net in Base 3 — Upper bound on s
There is no (223, m, 461)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (223, 2759, 461)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32759, 461, S3, 6, 2536), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 617552 411552 271728 613837 932395 565366 504653 527796 952900 121713 860179 804804 700810 531466 387241 207827 977878 349684 128482 422380 971767 166477 347990 996555 957583 509791 981976 925990 887006 993245 630918 189776 582529 832786 088282 296914 987657 041774 441948 746757 045557 769609 947541 221584 444069 973996 056986 793433 951717 127417 902539 108269 021668 973768 186333 081282 936109 795054 074840 329487 464284 087745 912752 541029 699470 703220 727382 619810 373937 203456 717074 747203 387847 337097 213332 962111 262395 384362 541836 215184 944256 480377 652430 141395 524813 082477 081871 471203 943434 691640 338020 195091 628682 691767 351176 578377 178510 140008 969737 205054 095938 195831 057163 562833 855920 221387 400003 964835 331109 844290 584913 438856 419396 070033 986045 814572 254027 885466 735398 126319 373346 712455 419356 076575 781696 739291 514150 519562 811853 884504 213131 596255 371099 565086 299548 802323 746400 318946 018637 909028 212391 373802 680776 715931 297012 228362 358665 680431 336168 294648 421919 561186 978585 477048 203828 042466 500604 546736 272207 996828 991419 815477 102383 859610 335867 769919 222329 892450 924916 376870 373349 617953 929492 092124 637098 718889 263833 216402 113402 924035 144475 375822 214197 346927 583131 111557 887772 152326 052304 441703 049058 793190 665126 797968 248240 408118 503970 612577 145065 680229 425440 690045 483230 727385 627443 659492 215740 136329 179071 341505 904739 108104 647816 642836 773942 129308 269939 407958 012608 374463 / 2537 > 32759 [i]
- extracting embedded OOA [i] would yield OOA(32759, 461, S3, 6, 2536), but