Best Known (229, 229+∞, s)-Nets in Base 4
(229, 229+∞, 258)-Net over F4 — Constructive and digital
Digital (229, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (229, 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
(229, 229+∞, 705)-Net in Base 4 — Upper bound on s
There is no (229, m, 706)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (229, 3524, 706)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43524, 706, S4, 5, 3295), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 644759 717351 117651 601961 440316 258859 177695 366090 475993 229862 744404 474525 649040 706368 289670 054603 709459 129743 461292 318316 227622 125423 938524 763202 937795 882206 152562 263210 647025 439824 233317 382081 462938 509652 544121 097252 154116 605199 152470 379526 759721 197124 545464 845333 565939 635682 031926 611470 689781 359691 652249 451786 063954 842365 677616 285437 875739 711634 088635 903848 897780 692622 109255 490838 651129 387111 613951 234622 138728 796752 442108 279516 388744 881924 268581 668060 114689 631398 870180 357065 751606 042374 842952 143076 227016 027256 008202 131606 514018 174636 333060 265742 679368 419628 979420 701126 324204 442279 921899 965843 127613 931333 759330 307688 779101 471703 491126 328125 159063 290122 609045 287528 547950 541423 965506 405325 479362 462836 738427 633034 701814 208412 965283 551916 915663 290082 060315 860732 997371 286853 097512 263720 062725 458973 978144 958592 110438 440014 847899 835996 986272 783848 166360 774368 318053 003912 000162 208685 206354 484071 261898 024110 841072 594260 247115 370517 789414 085575 187988 402840 220044 119400 018433 557588 061165 155221 243258 130924 427657 275039 223085 420213 863251 132338 774211 491721 488873 904680 695057 150851 055788 827146 540897 743173 448766 674044 972401 064004 925424 834020 953596 227710 319220 769547 502914 101683 262799 681278 509550 602090 152310 671540 676818 509378 804214 896950 266686 274064 330765 783636 800211 799212 999705 705822 932275 537348 898127 722663 704622 609850 133587 290566 202905 379926 759350 646940 367224 541474 823823 377584 101765 386479 053166 747758 519990 330011 865684 550761 043233 067830 078851 526255 975924 856181 525532 856149 573030 893079 557842 393094 397296 264956 902113 045248 467297 842881 031469 107922 238470 451510 390587 151259 417355 980771 282625 433546 999935 463896 995064 513186 797751 467212 784458 034071 685001 481316 459557 601685 399387 556874 229720 833019 912042 349234 851520 463692 414605 658766 378252 473107 534847 634678 231566 108016 551168 698081 469226 019815 481720 788509 977797 753545 435209 912550 744313 494105 799938 503782 301453 256194 749279 482271 538335 444925 993581 486267 528608 232260 758939 854074 640982 700725 935151 482246 108863 395898 295043 304041 788252 279809 153565 903807 554873 185678 156872 952816 889983 620002 768473 925410 232454 718983 934000 586088 092422 235643 927726 701029 544905 731928 238363 901272 216735 580160 / 103 > 43524 [i]
- extracting embedded OOA [i] would yield OOA(43524, 706, S4, 5, 3295), but