Best Known (169, 169+∞, s)-Nets in Base 4
(169, 169+∞, 200)-Net over F4 — Constructive and digital
Digital (169, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (169, 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
(169, 169+∞, 215)-Net over F4 — Digital
Digital (169, m, 215)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (169, 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
(169, 169+∞, 524)-Net in Base 4 — Upper bound on s
There is no (169, m, 525)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (169, 2619, 525)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42619, 525, S4, 5, 2450), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 70 625854 404239 394820 247828 065289 804928 103956 181531 134960 003464 160354 331311 684992 596978 514051 521667 606107 449425 450819 028384 897035 596971 159277 035584 511479 447001 186230 512001 407204 470498 402193 253004 892773 095847 441634 549700 883593 274507 039000 182055 167734 113075 172049 522818 270311 328663 130682 120454 790443 499151 938151 920566 451301 924714 203274 455976 765591 718511 510743 222042 707285 742532 258564 058315 808765 760373 525493 367166 922636 747479 321837 110966 923353 001198 081476 900011 550853 804377 308278 667515 297585 473325 497972 106122 365575 874558 574560 425432 576962 280239 373323 515760 310285 076557 205664 280431 106028 367911 008799 140197 253444 386872 809869 194595 127287 843388 406192 832308 396073 742928 811491 133475 208297 024216 634663 049124 380508 244219 147589 479645 823415 369755 869448 159806 344237 291943 577537 531307 758459 927992 333769 522244 114943 450234 991284 637226 282259 192588 679595 376620 955851 116692 332912 622779 372336 146753 867224 036796 930341 038841 573352 767010 723122 688700 866366 764473 430470 769585 948047 046052 492745 773626 575940 537165 059766 300604 702472 045649 629450 663403 072794 613061 044035 259123 262239 109268 661122 028095 626757 725223 041132 516664 523362 710417 735557 966359 281773 257126 361531 160867 875742 859214 422528 435018 087755 725428 592113 054331 425013 804074 715466 984573 072244 890608 003877 128760 191967 925210 387388 968084 956415 372671 627979 620767 333624 907804 215232 975969 971965 875430 916862 011398 260886 311949 668411 464703 602235 814462 425193 531727 661819 684740 101430 641092 520701 624644 243804 209035 507709 764528 758380 520194 113578 911094 484205 056683 071812 453550 613683 577407 313962 666092 325316 079771 791080 105266 299818 589219 189848 081846 303975 992729 796608 / 817 > 42619 [i]
- extracting embedded OOA [i] would yield OOA(42619, 525, S4, 5, 2450), but