Best Known (190, ∞, s)-Nets in Base 4
(190, ∞, 200)-Net over F4 — Constructive and digital
Digital (190, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (190, 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
(190, ∞, 220)-Net over F4 — Digital
Digital (190, m, 220)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (190, 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
(190, ∞, 587)-Net in Base 4 — Upper bound on s
There is no (190, m, 588)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (190, 2934, 588)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42934, 588, S4, 5, 2744), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 102296 876878 975045 265152 356385 814564 054850 012353 055422 323716 818944 939567 893919 320935 538661 032188 170209 558373 367149 833680 631527 731669 954493 465874 055287 759504 540748 422155 856405 990275 153468 106267 796702 000161 733487 211814 787046 678589 146461 500950 640535 146920 784187 167152 207866 799486 154902 022745 087733 019129 655456 230128 633422 912436 250941 866348 834458 354108 718050 620256 711200 031407 189187 582096 648686 277644 625319 748942 047910 673665 882921 041815 863760 387666 097993 567250 046084 189673 470021 272380 005920 556515 295230 141803 739891 962691 926438 875242 995845 113416 322351 338641 069731 585554 702158 604704 048315 995211 617598 078404 524107 104451 383152 486282 490689 547821 054780 333995 507322 639774 290791 839073 893271 372688 606459 580999 831846 796864 722003 876123 630843 140741 616521 873402 433342 450195 773751 548989 759844 554418 375935 639686 162871 855286 430570 397929 251422 085218 361367 812471 791353 349894 116361 309078 442881 272457 058603 869249 471728 380918 074471 898302 905850 324597 048044 088058 432828 919058 801884 003873 041914 743757 252785 865409 724938 575093 728993 905886 930860 750430 974038 488707 118459 622721 508793 836550 321680 120469 376477 550700 655765 547745 307662 203676 020623 383686 644938 365163 596369 961492 405779 803666 179573 702668 383439 853959 584683 398663 622220 032498 598116 710345 249860 658256 793702 286335 497762 540185 775574 585628 313415 120979 492500 192249 622604 954150 834108 118155 588399 997514 792150 460257 858814 472533 621275 801681 266015 051171 102853 255945 178669 286387 204013 785383 609381 218274 548671 916946 463223 696311 327333 207579 397086 881641 321887 358614 021179 220700 729226 891753 585331 353201 094941 661298 293160 219890 638613 826713 157980 444507 390833 418974 206735 317961 551778 212384 918965 677052 821435 551332 119350 062457 977586 580375 604213 344829 326856 062498 318372 455899 773312 494373 547200 937754 121489 486265 226832 120775 814937 645363 168212 641218 174582 538012 459008 / 305 > 42934 [i]
- extracting embedded OOA [i] would yield OOA(42934, 588, S4, 5, 2744), but