Best Known (260, ∞, s)-Nets in Base 4
(260, ∞, 258)-Net over F4 — Constructive and digital
Digital (260, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (260, 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
(260, ∞, 321)-Net over F4 — Digital
Digital (260, m, 321)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (260, 320)-sequence over F4, using
- t-expansion [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
- t-expansion [i] based on digital (257, 320)-sequence over F4, using
(260, ∞, 798)-Net in Base 4 — Upper bound on s
There is no (260, m, 799)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (260, 3989, 799)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43989, 799, S4, 5, 3729), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 91061 142592 428490 068140 367554 869534 559760 963880 552701 163932 534154 455829 262104 678775 376640 634299 668749 554400 732048 580813 497524 640207 040265 220082 244062 633277 496783 862276 589562 727190 260153 499933 860630 742413 559410 397096 634082 779068 877772 703017 749585 169035 723683 364641 895578 866948 863131 514223 301227 045608 191473 376590 705327 584885 589431 909823 281512 246559 730614 740477 658905 443585 786292 042054 160919 789979 163226 149807 688355 863566 476998 740800 319386 338746 566318 586542 494135 166401 245216 893128 912733 827515 254988 265979 843819 301556 995775 979052 499834 137704 095496 579671 215032 141909 448937 760241 012859 428810 789546 341765 837376 703348 290833 893235 873716 541144 986160 113346 401600 753052 680012 225772 372064 758443 176965 140545 466036 758891 787357 851252 925450 523722 983286 227747 288442 602186 120019 983757 667559 794346 447000 248252 670222 012874 223166 320331 354359 553083 392733 430059 502048 281266 518294 110303 788294 139542 982968 523893 521118 190354 673462 180257 801151 671863 225939 369208 697312 481940 901117 443311 266913 081987 638671 046129 986557 595265 267819 519209 502139 886854 359359 418617 575531 924775 625340 297947 351833 380260 577517 021941 709128 675492 062991 478169 831574 346830 886727 896730 946343 262570 340527 972805 520505 286126 563413 082676 769126 032426 178031 272690 919418 151368 600893 065644 333996 421129 336825 070799 278783 215636 732623 237605 218394 145363 394202 122386 637260 432280 217096 584358 859231 490478 797478 689802 622238 971573 137191 917085 758534 596703 092708 519964 381399 958874 025934 983837 098651 121806 833268 231171 850838 782379 246452 498449 679888 669134 845198 521878 986789 524913 338330 403547 814619 973208 559853 205421 999414 249919 747624 461952 827687 569737 702304 368684 460263 433327 164125 730470 445580 924846 010824 183013 631016 884199 522526 529490 387950 799911 120473 633051 957612 942671 963583 705676 195294 855890 448508 494907 903843 545363 082087 842561 663159 540287 512281 146694 319721 119009 787984 459272 920345 435467 251754 602345 965697 827591 659869 031574 282388 200634 060673 030717 818586 183254 454064 344512 310544 314085 012961 489653 505229 902070 802303 295550 012817 822700 795216 981025 002413 843022 563252 967652 036445 069696 993329 151798 575463 733239 071418 567592 296498 316616 244022 033953 902465 126478 305994 520606 341278 799114 165137 721842 536132 033569 746401 448685 309277 097447 219539 942632 889396 913244 497660 313579 244005 674521 982315 680851 335202 422823 781759 736739 725727 439062 631130 815959 282047 902967 398932 085106 395716 804989 893838 617327 994958 454436 211462 918080 161837 244554 704189 558464 151373 743038 439183 193615 061066 725746 224231 215332 851712 / 1865 > 43989 [i]
- extracting embedded OOA [i] would yield OOA(43989, 799, S4, 5, 3729), but