Best Known (189, 189+∞, s)-Nets in Base 4
(189, 189+∞, 200)-Net over F4 — Constructive and digital
Digital (189, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (189, 199)-sequence over F4, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the 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) = 161 and N(F) ≥ 200, using
- t-expansion [i] based on digital (161, 199)-sequence over F4, using
(189, 189+∞, 220)-Net over F4 — Digital
Digital (189, m, 220)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (189, 219)-sequence over F4, using
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 181 and N(F) ≥ 220, using
- t-expansion [i] based on digital (181, 219)-sequence over F4, using
(189, 189+∞, 584)-Net in Base 4 — Upper bound on s
There is no (189, m, 585)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (189, 2919, 585)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42919, 585, S4, 5, 2730), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 858 478075 345556 135540 537611 498783 642198 067039 420210 160176 970660 943162 402624 619851 937209 276195 817921 631806 444228 578319 623697 230122 197827 112529 038004 511892 686884 287845 659241 409951 437327 697590 641388 527463 211283 785195 803132 694706 061636 468074 568759 929761 263522 553961 897960 515538 696426 551797 707420 679384 867664 479354 726850 213021 461609 253003 901597 172908 202778 061732 334100 852133 671387 022862 839732 814379 435218 770136 661480 524581 948304 766947 660180 713347 434625 400749 098835 551394 952487 925662 811206 857606 517350 886134 059253 132912 933735 519359 864573 476259 294282 131339 761942 862780 287376 822451 247550 769425 912709 469451 420722 658762 042174 130061 967144 331886 146120 533679 999447 250216 115013 680406 565266 964713 747802 990130 845908 814500 621059 800268 459518 166377 115995 670072 031989 297740 609834 942826 115555 728579 312903 590392 036171 354353 756390 176509 824352 955492 679248 097439 125615 859718 651373 744387 767046 331376 028668 121309 301168 686465 128241 281022 004995 231062 041765 934797 818173 362568 787610 500880 990336 804231 373295 182710 682142 911385 266002 348057 078052 672133 449763 443352 757843 808830 150147 880655 310649 918998 359916 123212 627374 421714 854265 238916 090619 717776 008321 356035 613306 987322 838616 511432 608497 071925 308655 295915 137325 520196 890527 508089 372906 821262 376991 692664 171386 623465 295391 533299 207605 900683 135278 331999 505012 444538 094033 887073 225964 059465 594982 319369 140391 812331 344496 592370 412312 829053 047331 034625 160105 621089 698758 106257 756282 448162 071773 063937 582732 067110 873536 211278 958593 932801 243324 571986 405906 192758 839572 957736 732605 531864 999208 758178 245070 781530 572314 360202 182199 834950 685419 767735 613297 437280 513846 108716 124247 841962 846986 286851 099540 136026 201597 022153 615945 659366 591953 924157 206373 650376 270990 117877 609542 652578 251746 418130 686979 526088 146584 390177 949762 774671 934731 793383 074304 098304 / 2731 > 42919 [i]
- extracting embedded OOA [i] would yield OOA(42919, 585, S4, 5, 2730), but