Best Known (206, ∞, s)-Nets in Base 4
(206, ∞, 200)-Net over F4 — Constructive and digital
Digital (206, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (206, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(206, ∞, 258)-Net over F4 — Digital
Digital (206, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (206, 257)-sequence over F4, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 191 and N(F) ≥ 258, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
(206, ∞, 635)-Net in Base 4 — Upper bound on s
There is no (206, m, 636)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (206, 3174, 636)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43174, 636, S4, 5, 2968), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 2 818567 860915 441737 413000 210117 572864 087996 456314 070560 480493 188150 323902 757789 828217 930741 886861 728793 033078 305448 828634 890589 413342 376730 157116 159414 675790 173751 688856 819211 933601 235677 864129 406692 976193 026526 843025 757371 048167 021061 267804 426965 002718 595229 650769 128583 637914 662738 904218 649978 356287 159217 161236 873049 720875 282248 705404 629835 216187 801555 398810 284311 993275 498292 594831 729643 604586 079862 209853 000077 037741 759665 191757 202450 578716 645177 554846 018969 110896 093043 858309 422899 674767 108114 035262 692396 515454 355293 162601 158771 214953 459800 388378 997551 708004 577210 859457 814142 785398 106010 402729 832999 105729 558763 027004 307496 537253 257767 976092 110097 833333 852316 574330 865677 016646 103115 796566 284874 246340 073582 981111 310303 553225 494667 765244 251076 078205 923223 937933 290086 875646 301419 152982 745300 192902 499305 979394 948906 663320 352322 044733 482307 140153 620372 975155 876760 475622 505616 326604 123476 039179 314901 043895 199368 124967 183243 384567 510264 702524 093711 733053 708028 083897 873016 744989 946784 477129 515277 023431 818256 421862 955888 423370 493369 827866 877598 456125 339271 900414 822227 621175 902723 872037 040147 610401 453963 511660 782639 194488 285820 358833 687656 928434 055780 487027 406229 276585 943189 532854 003026 209540 841545 446243 482471 815398 461716 681786 214128 627326 788916 272180 619922 371626 503905 146856 338984 967230 186554 932539 034051 462082 551859 456075 481389 662630 912032 809178 716773 420756 201718 547128 932899 041947 743878 238361 363161 421212 182684 252390 998042 461278 622316 307591 279150 387404 510312 185214 348265 544989 454152 719062 206307 475573 184161 907160 308595 108627 035445 569823 110073 441810 483353 406334 882675 789521 250478 463008 370224 173910 219966 790403 557332 608982 617389 397204 249160 243276 654768 886061 930475 572015 980302 655673 455228 266512 686250 714984 283631 416739 710924 588710 799898 696498 348772 914403 925052 090731 022585 819613 020782 036682 590343 707634 182383 540435 915237 204801 578976 753150 517163 584422 512983 945302 181604 202019 848330 460630 943967 829125 234688 / 2969 > 43174 [i]
- extracting embedded OOA [i] would yield OOA(43174, 636, S4, 5, 2968), but