Best Known (195, ∞, s)-Nets in Base 4
(195, ∞, 200)-Net over F4 — Constructive and digital
Digital (195, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (195, 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
(195, ∞, 258)-Net over F4 — Digital
Digital (195, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (195, 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
(195, ∞, 602)-Net in Base 4 — Upper bound on s
There is no (195, m, 603)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (195, 3009, 603)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43009, 603, S4, 5, 2814), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1306 091888 822333 850966 857073 727467 242718 259817 480160 322280 330090 145791 239421 379070 662057 669896 755133 696741 757788 199638 313998 115519 143697 712936 908360 252127 154498 252871 908037 292914 811967 240969 170418 717826 625196 003590 283286 315494 236228 034822 995038 713673 989243 015366 942553 514147 379624 703299 499765 663502 548925 347917 442970 017952 014721 922134 678306 490416 911845 816980 054156 616376 374452 469722 376969 305951 902666 525308 202463 867055 742411 345630 198372 695899 544506 105606 290814 909489 507078 185894 486234 972443 247397 332695 904945 335351 793986 936319 869867 554894 107536 389868 444855 655107 914331 815516 674579 791781 545318 857601 139695 227065 585429 191162 130646 842504 223813 250464 902962 778103 833920 830701 362681 255180 468252 935370 977816 338610 834273 311837 397102 113706 403294 946483 865959 574876 698771 692530 362077 446042 461599 375953 952405 300717 714600 061964 988040 638642 703415 466251 534376 249878 575898 775311 162090 633868 747597 867468 058089 039212 344931 895030 538792 273706 834479 195778 370263 603408 504756 829002 808682 305908 515407 014679 243626 253165 471469 414511 929594 971238 046934 820109 140736 059241 258521 316747 782578 710403 261448 818496 425365 223977 334042 102191 062714 574269 259557 770975 690138 495032 562790 159347 644298 197098 876792 558789 024847 986410 592500 959605 065465 012904 529364 941718 078295 915796 060003 357706 686685 279435 217280 884101 513479 275630 469475 391554 967138 669460 594177 343192 364133 833148 046650 710931 143194 072931 741716 402699 037099 609857 114951 512669 005554 582414 161402 876572 660102 453859 019046 831539 074197 100788 690383 138962 267648 322776 096975 100197 885108 927603 484627 525033 096375 741670 619772 284025 704501 014444 645920 450528 893991 425439 879274 521449 272585 102055 043597 771172 956420 099389 668902 260443 915342 079553 329190 431689 526461 206350 759992 609887 801613 924632 436927 518328 804930 446922 478985 373297 739965 652873 197841 542388 674064 650704 029050 450237 821464 352211 505052 478534 254037 823859 458048 / 2815 > 43009 [i]
- extracting embedded OOA [i] would yield OOA(43009, 603, S4, 5, 2814), but