Best Known (249, 249+∞, s)-Nets in Base 4
(249, 249+∞, 258)-Net over F4 — Constructive and digital
Digital (249, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (249, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 from the second 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) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
(249, 249+∞, 301)-Net over F4 — Digital
Digital (249, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (249, 300)-sequence over F4, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 234 and N(F) ≥ 301, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
(249, 249+∞, 765)-Net in Base 4 — Upper bound on s
There is no (249, m, 766)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (249, 3824, 766)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43824, 766, S4, 5, 3575), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 504116 741855 700317 603780 302367 835680 051463 503013 204658 174191 911126 004117 796884 403555 561993 757212 365391 258170 468484 326676 610331 424891 925960 390115 632380 672372 629948 908904 447741 116626 949013 480795 622475 549441 394434 926879 408147 897275 183939 555986 914414 191566 870509 538036 981608 621481 369084 224595 286523 651081 559610 615054 718435 677409 325709 080395 078518 602821 674615 360257 676161 760345 920000 770878 705326 613557 768552 760115 793904 721862 641286 415353 993712 146452 896330 066752 193302 847968 250386 499863 981504 475755 585980 513960 675965 224674 230415 200279 039643 553639 768918 527747 113820 672118 459761 185033 419235 167713 519046 962134 306408 331981 591500 287428 713202 455235 530662 717984 106684 226162 672345 773188 542412 417620 493391 648314 599446 404787 129059 772374 223970 230050 656005 235338 645405 352653 461263 217566 632961 294196 724131 620781 226791 540204 734774 000802 682736 796653 183252 741826 545149 653150 764479 483832 551699 628297 387821 719398 829725 325106 914334 680501 615971 567830 239830 131515 701598 250156 622364 060220 350275 542023 800544 111546 637333 486296 090479 595413 844374 629781 003834 936676 875710 789908 873767 591468 406442 482414 831664 206110 823871 987972 105560 978274 643618 178923 140169 288227 784358 414911 111692 588404 873934 313144 949326 551076 562672 163710 459817 566593 491037 640689 215088 647774 314840 493072 820240 001040 572274 991152 653961 842113 877263 607636 049910 870179 165774 999252 562725 768770 980678 979062 640308 289526 300707 875830 852544 379464 341950 159134 906262 551848 288156 251323 198285 322855 147109 843149 044775 348972 641954 624126 973267 482773 015149 542681 920971 606279 082271 313256 347763 181386 627909 552967 009266 266318 148755 753210 912591 496789 169012 671973 575765 768822 360433 174619 408393 103392 318176 417123 696516 459807 044609 093358 291813 283052 275306 030455 724241 331459 411430 258408 832199 912100 639930 224531 985140 100789 660877 865669 646550 762769 737852 725903 709203 544492 321948 057536 236020 933233 037746 212956 234285 471225 408680 180341 005999 865360 667556 636252 722751 618843 558024 194171 717155 795737 561159 677016 907123 050724 027674 066041 487865 029841 995822 710149 956330 009912 782273 181330 024954 428801 909539 769459 036678 440058 945237 850463 277339 779314 512660 287861 511391 283608 060470 795008 449656 479075 125290 977106 157701 809196 956848 413783 687761 862447 549114 407159 569232 884103 972745 499620 138033 365095 528531 128946 155014 868290 824465 421738 328317 685526 523205 720868 505870 392734 002877 651239 250873 432086 738132 483452 299494 031360 / 149 > 43824 [i]
- extracting embedded OOA [i] would yield OOA(43824, 766, S4, 5, 3575), but