Best Known (257, ∞, s)-Nets in Base 4
(257, ∞, 258)-Net over F4 — Constructive and digital
Digital (257, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (257, 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
(257, ∞, 321)-Net over F4 — Digital
Digital (257, m, 321)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (257, 320)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 257 and N(F) ≥ 321, using
(257, ∞, 789)-Net in Base 4 — Upper bound on s
There is no (257, m, 790)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (257, 3944, 790)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43944, 790, S4, 5, 3687), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 18 439850 526344 244907 410263 230227 820450 582201 007558 209490 374193 796238 562210 978996 146141 788248 385823 174299 002328 223354 600153 201221 200319 490955 465751 023917 607458 900767 460340 676899 360406 176266 695933 946287 895059 888272 374964 362534 438814 937820 871061 486306 395990 161602 207662 679603 765774 192280 769449 800821 301322 350323 781846 405433 822189 601152 305122 876647 630147 506948 550744 084865 996017 349685 917419 714658 439875 399223 070784 005417 682404 942621 582363 185098 678425 879252 199782 150795 281309 512268 794866 646434 255061 429451 423076 884094 764682 749037 756630 985118 776128 240543 131292 016315 963283 818619 270171 688950 697518 902022 766574 032003 751178 097942 631770 734957 633032 010778 583087 572834 741747 407233 287841 631852 569678 349413 011505 249637 797393 043927 562368 066230 908316 669886 687313 280588 321777 445559 053854 086756 354740 829068 493660 868327 985509 879352 625422 423557 102481 542788 267360 020265 374573 879648 323037 167988 586716 544641 830357 026727 543315 554180 107474 596981 059261 466311 660309 697531 610337 162111 522953 011945 397397 855162 781189 332976 598768 761463 372070 498080 000135 003789 942934 008790 494732 864764 866780 965050 086971 950166 433215 381554 656061 081477 227650 501419 101163 804170 755806 196098 608786 957245 209346 782539 990161 838340 470044 095052 667058 499759 582087 219040 205658 441054 194584 453809 703103 608244 087230 522946 961773 651448 143832 963012 791975 661272 204744 545357 839635 268822 608889 982295 458909 468372 944984 495272 778056 938553 341617 797683 797681 191720 818017 580386 070562 983394 722863 847949 295206 889650 255915 235469 804957 669315 596044 246303 096463 355968 246971 777598 985130 308168 598092 714459 263497 826826 561030 951391 252171 306092 715840 847193 766402 757724 362777 338416 364075 069750 081915 561152 357713 774381 234175 500313 991216 538338 211292 393280 065540 812555 581689 227327 500180 283444 016296 271786 503485 056238 645574 816793 928272 476533 375120 683552 740333 621860 501258 463103 132983 953448 680358 949762 983655 272936 680797 521912 868874 569777 218064 644720 032715 531697 884426 495128 981299 470300 269253 232334 502880 715958 956691 922601 253985 722535 046098 664224 843899 032608 911365 606791 379194 819599 470599 212704 416530 767390 653771 295252 001312 442709 128280 481734 134574 767989 743557 898212 809123 423853 505764 030604 395190 088933 236836 913031 234808 043226 746666 256422 922021 386601 383606 901807 994088 007783 580910 575072 877444 095234 085415 055709 855549 018594 021707 505537 758512 289513 603268 301292 420717 116668 103476 191504 313220 766549 696501 707530 289028 578222 017006 813516 972750 309030 868474 251284 802429 963108 089856 / 461 > 43944 [i]
- extracting embedded OOA [i] would yield OOA(43944, 790, S4, 5, 3687), but