Best Known (236, ∞, s)-Nets in Base 3
(236, ∞, 112)-Net over F3 — Constructive and digital
Digital (236, m, 112)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (236, 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
(236, ∞, 163)-Net over F3 — Digital
Digital (236, m, 163)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (236, 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
(236, ∞, 487)-Net in Base 3 — Upper bound on s
There is no (236, m, 488)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (236, 2920, 488)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(32920, 488, S3, 6, 2684), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 4549 427729 689467 772833 245944 728075 535956 908194 330249 528968 064575 349261 184411 562226 984635 064452 390927 196278 907688 404213 332849 918870 571009 392670 415989 205205 721261 973969 493346 669831 285131 379804 962448 424259 869595 365754 072019 674359 622913 886121 574258 961515 244819 598326 835495 046866 361166 682087 108818 568688 767671 802180 955197 191035 845565 611191 363399 386599 991092 544710 805261 488255 232452 924483 226084 956684 700180 796071 748374 934676 718930 772011 042977 249665 509363 846877 309751 717939 454944 980102 346442 659200 274219 932415 937860 965291 963832 090793 617737 780554 139918 114123 719356 321162 984458 460460 234031 006450 167488 754627 718419 322736 412665 737379 836503 220197 688607 064769 639729 733328 353872 947658 701769 000091 616905 644815 095942 355159 828464 610605 145143 674645 020025 698501 972443 182772 377909 354369 760339 125694 922166 656985 252097 773373 530858 641285 293009 524824 470985 759309 053438 101271 605590 808086 253950 052937 045809 761305 450295 644589 035664 619417 907376 802808 936812 317213 290888 353889 083894 888340 516224 653460 432735 012135 730806 596032 098644 825456 386337 524325 472947 645936 154344 283772 174365 863918 834136 755382 913620 575425 201140 275801 517156 657688 956358 263265 480500 223362 179917 664514 660309 465250 738592 524342 454258 590979 204400 006724 147368 901595 901938 025193 210597 071172 615579 522846 036347 821160 270402 099996 085712 729225 114220 228815 376819 801283 045078 131360 401730 472484 770227 952620 698285 097383 726232 247656 349946 448352 353546 109457 637309 691431 618691 / 179 > 32920 [i]
- extracting embedded OOA [i] would yield OOA(32920, 488, S3, 6, 2684), but