Best Known (160, 160+∞, s)-Nets in Base 4
(160, 160+∞, 130)-Net over F4 — Constructive and digital
Digital (160, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (160, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(160, 160+∞, 215)-Net over F4 — Digital
Digital (160, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (160, 214)-sequence over F4, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
(160, 160+∞, 497)-Net in Base 4 — Upper bound on s
There is no (160, m, 498)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (160, 2484, 498)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42484, 498, S4, 5, 2324), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 37622 225581 843019 140406 508442 630817 874269 961016 511429 046160 987816 297989 019659 752826 356654 067205 218276 267854 978899 816702 744515 889965 010891 448788 120521 063933 243305 243985 386103 500981 915647 636790 035144 258745 771421 672059 399827 939116 763213 609860 542314 285186 750510 702479 711477 875484 151731 155903 248794 882571 370428 763012 407930 021838 111122 977160 820658 322037 392908 873608 717425 161769 318998 439614 272065 121328 541279 495311 776287 407146 807267 566750 186987 994271 951709 716184 907114 497582 810271 189379 451684 643574 204170 812218 122324 832046 895929 676584 374177 854333 553177 123572 475053 374995 261099 617158 729878 693867 490647 554279 123587 516341 282518 173257 322103 217389 574070 112186 759871 225271 206046 894684 772818 703805 620262 225363 445933 265796 546703 590054 497615 051245 465185 319857 781363 616138 765600 945064 103584 423617 303577 749623 303147 666955 580312 387156 535576 311546 512284 449771 917529 847145 139516 359149 622413 913594 530351 001592 202108 213243 771110 316957 956500 162951 254499 136705 503317 504794 261075 745298 976158 624382 285665 680262 261203 698720 543854 933340 459579 359443 372068 916601 264618 298242 090093 547271 028112 565733 735708 804538 653170 127216 282230 244203 626379 066470 827902 132504 982071 232903 981525 526765 296623 078175 174266 619191 929206 236492 287840 394735 516310 223339 095307 354897 030868 861328 345867 501731 358550 376681 881507 207571 891286 559909 446159 562229 446948 073971 679227 400443 401577 363031 536250 434646 170733 851742 274266 674895 192989 169039 507913 306048 490965 676801 678605 340683 110617 921137 761059 570656 567715 619812 303212 049349 203879 240531 287105 842812 966890 635264 / 775 > 42484 [i]
- extracting embedded OOA [i] would yield OOA(42484, 498, S4, 5, 2324), but