Best Known (239, 239+∞, s)-Nets in Base 4
(239, 239+∞, 258)-Net over F4 — Constructive and digital
Digital (239, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (239, 257)-sequence over F4, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 225 and N(F) ≥ 258, using
- T8 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) = 225 and N(F) ≥ 258, using
- t-expansion [i] based on digital (225, 257)-sequence over F4, using
(239, 239+∞, 301)-Net over F4 — Digital
Digital (239, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (239, 300)-sequence over F4, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 234 and N(F) ≥ 301, using
- t-expansion [i] based on digital (234, 300)-sequence over F4, using
(239, 239+∞, 735)-Net in Base 4 — Upper bound on s
There is no (239, m, 736)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (239, 3674, 736)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43674, 736, S4, 5, 3435), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 10 414205 941067 178638 652124 412570 769922 847064 719217 302485 099958 959213 718662 230647 547396 634303 082156 544953 041769 154711 028321 265562 570369 735751 389038 211574 643698 951502 429897 431288 794493 337861 464166 284385 167494 288915 277901 011164 366568 357919 700134 931428 147489 445440 730988 763233 650061 365935 039173 535197 499044 281987 274828 744875 447412 196230 647523 331264 487812 319282 734706 508758 150994 251439 863183 012200 260592 029086 791896 032928 335936 888937 187611 129801 491161 139805 416414 323251 414246 950411 368009 692334 025352 468852 422481 474906 896545 602587 635137 309430 634194 049454 616453 354915 142539 990445 725523 504800 047065 997654 112377 259719 577389 964804 240810 242607 078078 620443 203665 368486 331248 656883 660924 939961 850610 413003 525362 394784 599117 677857 776583 346645 402721 342994 031505 664879 542330 116007 512416 404684 536921 576519 843746 577539 896649 531438 960811 716764 237178 417498 385927 232312 806494 568482 505947 966917 656390 703530 229924 569464 467489 217276 610592 199455 978279 425848 544747 803055 071914 171530 907712 202102 102632 463244 310396 683297 913602 650485 231687 944922 820470 225482 205494 429343 414759 493640 152763 409039 263897 512420 146620 113010 152016 048977 994983 903350 995791 393043 738023 469586 250382 228446 934803 436886 980087 080570 177807 775058 965388 741375 560969 120990 895673 611720 801381 796921 699359 592626 286249 884045 291879 452321 260651 895195 632433 924756 284868 146088 564081 276414 651162 710821 996728 101487 907985 068547 176920 407029 958968 906026 197998 779442 839048 385757 981052 995605 381302 506210 604362 930935 199806 716721 003346 950227 133056 826311 869788 396637 138221 372704 228356 246696 471437 625672 908076 623019 895908 881238 581088 920724 453590 654627 706043 245401 658990 903675 805079 650970 531792 747749 267863 248141 379909 533593 969823 108129 338333 158731 901773 533129 362136 145043 570648 676702 118045 425588 907426 982199 861457 215039 963464 766416 789628 284268 191141 745002 331576 508434 622625 443457 374761 127927 687531 216521 295718 890677 617045 493913 761040 262353 077987 434758 310507 496943 191974 940145 342787 217755 284183 030850 634763 740295 701214 537994 839129 361405 163055 836154 020154 358413 516794 161109 331672 411557 087620 601250 294811 640766 949965 705056 304665 612885 744838 459740 110563 431041 319972 233435 580945 353906 734644 050385 767845 505293 349411 549163 509996 861041 846835 414273 708934 814719 042874 604332 906894 036905 878473 187150 759953 694720 / 859 > 43674 [i]
- extracting embedded OOA [i] would yield OOA(43674, 736, S4, 5, 3435), but