Best Known (157, ∞, s)-Nets in Base 4
(157, ∞, 130)-Net over F4 — Constructive and digital
Digital (157, m, 130)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (157, 129)-sequence over F4, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- t-expansion [i] based on digital (105, 129)-sequence over F4, using
(157, ∞, 215)-Net over F4 — Digital
Digital (157, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (157, 214)-sequence over F4, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 148 and N(F) ≥ 215, using
- t-expansion [i] based on digital (148, 214)-sequence over F4, using
(157, ∞, 488)-Net in Base 4 — Upper bound on s
There is no (157, m, 489)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (157, 2439, 489)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42439, 489, S4, 5, 2282), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 30 497254 008304 082179 726729 308191 627557 972563 557716 755906 885831 793049 162186 083754 640539 379913 736611 119107 015314 324340 795914 589730 257832 695091 155369 087195 851412 122598 858878 328887 683030 637706 058327 121095 621634 861316 764008 909283 020866 677855 371738 915919 483643 889564 249617 381912 699687 803815 888292 940788 074065 351617 886544 274891 791618 898930 656915 370952 653653 214961 347351 770130 228680 422278 199146 088278 554420 949075 745162 799557 240129 758159 869375 544449 163713 482183 138257 789187 385662 307792 246108 024363 289408 774592 544157 061775 400518 215421 497909 158050 733746 848646 228485 464160 803713 466874 287303 026928 740831 628172 297013 364591 048662 389332 686138 006482 103256 940316 086998 809880 550638 568782 897207 841352 769425 866609 714903 146159 563792 877011 579663 970192 151150 080585 982346 453499 951151 394365 428650 472585 209915 675697 484134 834346 923641 339737 494234 887630 612615 860112 509204 846276 363934 477431 175059 093291 333903 558334 431674 829430 659385 184809 098287 594432 703426 970120 926956 870837 987055 704373 101434 286500 315880 193076 440053 567941 740263 628189 557785 701676 414540 340812 318006 687607 547425 513787 280976 732561 908911 307736 931851 645889 464902 675963 480776 287218 913069 441371 764576 610795 151240 957586 957234 469838 332293 771261 008897 654614 619652 187591 254606 534841 869606 753437 882638 017548 393331 210008 054140 195119 199555 647452 152903 908710 973589 986453 945692 966002 003599 576196 350097 153304 288605 903426 058871 343240 380366 597726 164371 769708 925031 296436 197189 048555 049560 589874 813222 118414 891561 978935 452117 191414 470455 116461 955467 968512 / 761 > 42439 [i]
- extracting embedded OOA [i] would yield OOA(42439, 489, S4, 5, 2282), but