Best Known (240, 240+∞, s)-Nets in Base 4
(240, 240+∞, 258)-Net over F4 — Constructive and digital
Digital (240, m, 258)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (240, 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
(240, 240+∞, 301)-Net over F4 — Digital
Digital (240, m, 301)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (240, 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
(240, 240+∞, 738)-Net in Base 4 — Upper bound on s
There is no (240, m, 739)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (240, 3689, 739)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(43689, 739, S4, 5, 3449), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 7448 122935 780481 462417 969687 766594 286988 786894 924278 509055 694835 154191 778683 889333 086714 528363 475962 912354 579835 744020 424976 019628 973586 251241 499474 539986 120309 705944 229822 324722 208078 716435 471196 213334 123251 798167 153816 401631 434726 149128 764854 536660 188975 529942 960645 443455 939358 306411 820595 124175 138158 942811 577925 655718 208626 781039 180104 004185 337534 826187 674878 763135 867395 067943 550934 573597 015870 563489 898774 189167 210410 060464 937737 069600 350403 991883 725038 447163 894195 259259 212900 422433 695196 181056 663705 173808 062484 596190 489506 352144 789734 456950 154090 093980 686622 824344 088278 663893 721232 059331 904834 492192 753023 782391 243367 634433 636125 405577 265423 176904 012289 978303 508087 099150 948009 747644 451983 781803 181802 020879 881362 131994 654843 861647 494164 760065 197572 038518 154331 239346 988215 725321 390265 437891 751504 084381 503992 330479 054302 029589 477885 282767 089010 364589 411697 314333 034773 581994 169184 431247 545263 750673 613102 901044 025347 766828 332319 417473 111091 061107 238017 465997 823975 847345 416969 498515 765160 571484 267523 865053 241097 890560 836535 726105 192446 810696 914959 652552 562035 287466 858148 012179 142988 715492 526544 561709 373407 991921 425103 033668 180364 342560 858425 310493 911511 574475 204264 496467 519847 129562 224633 354115 171385 051865 845184 402623 999499 347643 195561 852211 455479 125508 374083 616790 842858 215857 039340 123528 940695 789107 077634 408697 587848 819524 858605 735081 820821 550168 966227 735381 612073 181420 416830 270027 257149 198858 601393 314019 517830 073195 723068 098891 275818 637073 589995 201160 412093 616428 937435 540217 489232 715936 391952 561450 115179 321183 028958 250061 986108 817026 950960 094270 640487 825697 210168 846920 865326 876958 128871 998991 066545 434687 362463 311525 992156 919453 703071 603972 685738 851558 315271 074015 564648 309863 952615 987205 841225 000459 554570 144400 062722 796843 606441 858178 637537 115468 221290 062284 588942 958697 241008 695328 501967 304864 455387 160992 033314 273172 533786 867480 926536 486666 174388 113892 144788 908828 202974 569274 323345 641049 104206 366401 533041 922548 498690 113395 265190 027405 007252 927769 227265 730209 290539 010907 421997 023236 875683 316588 447195 796351 370882 810672 414793 727353 459130 111649 843089 066626 745705 272602 246258 609253 440602 463657 552286 330015 805456 044440 162851 979585 454211 730295 758222 363688 873850 464359 630374 321908 361899 176649 293824 / 575 > 43689 [i]
- extracting embedded OOA [i] would yield OOA(43689, 739, S4, 5, 3449), but