Best Known (196, ∞, s)-Nets in Base 4
(196, ∞, 200)-Net over F4 — Constructive and digital
Digital (196, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (196, 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
(196, ∞, 258)-Net over F4 — Digital
Digital (196, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (196, 257)-sequence over F4, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 191 and N(F) ≥ 258, using
- t-expansion [i] based on digital (191, 257)-sequence over F4, using
(196, ∞, 605)-Net in Base 4 — Upper bound on s
There is no (196, m, 606)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (196, 3024, 606)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43024, 606, S4, 5, 2828), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 466900 490209 357522 884936 396284 632666 792777 732661 498072 105239 847954 279476 679261 046673 511709 694614 944360 524325 704573 688672 562646 699251 675196 485808 262486 370914 150355 009863 720734 561723 036525 301259 748537 172387 737447 901818 132344 934347 099999 629979 622774 138071 553603 360419 069160 994546 189107 562109 663290 257463 436962 495361 469739 728495 595098 029204 223109 604926 371983 324757 940410 534143 890131 111101 689981 600434 929485 474360 855826 987105 983478 106661 281493 814812 808528 400385 029380 618583 666444 558724 351987 999807 778796 235344 122544 095083 822933 456546 395886 394088 515085 371347 549481 338817 250674 772229 589802 304653 135330 762205 171601 390398 380783 361249 344213 790849 727040 824225 673067 757104 621360 336709 749594 012461 006216 490514 055148 279729 861904 973639 453583 271678 094270 173309 601979 939384 793797 206573 965689 370538 320742 292797 150930 057952 154503 351585 666479 738908 265363 512744 631984 434570 000918 740098 053593 415080 669402 642070 047956 305718 336712 386983 753139 892127 499900 884134 855316 347991 471483 120876 475591 054762 424071 995236 350397 332686 605070 003549 053146 458751 940210 972964 251427 038790 994800 932460 453270 305417 507007 645041 431717 030289 168642 288265 789461 519597 513444 934122 029376 442858 835064 231166 616579 249919 193575 426717 870449 041116 506127 458247 348116 169886 092466 219288 365498 680655 717041 479377 895327 918096 294879 114756 648268 593504 955271 459135 387138 994008 636379 789699 872580 761302 192878 950464 236039 952936 283827 937047 919120 023816 226672 756292 751263 069387 067745 437002 588070 216728 739190 285374 281959 387804 020236 004087 801381 340160 763113 877913 022451 819732 651231 865081 485082 287131 662614 512451 090865 573684 789062 559519 092759 765560 409514 776915 340104 720743 102227 549932 257352 694927 434313 684879 370953 908737 876690 885772 436327 631119 908384 957327 946583 534076 538975 048856 690092 061287 618014 157917 278722 479801 472367 947684 530681 353824 505562 044748 511421 690290 891932 422457 925774 417377 382656 638976 / 943 > 43024 [i]
- extracting embedded OOA [i] would yield OOA(43024, 606, S4, 5, 2828), but