Best Known (186, ∞, s)-Nets in Base 4
(186, ∞, 200)-Net over F4 — Constructive and digital
Digital (186, m, 200)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (186, 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
(186, ∞, 220)-Net over F4 — Digital
Digital (186, m, 220)-net over F4 for arbitrarily large m, using
- net from sequence [i] based on digital (186, 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
(186, ∞, 575)-Net in Base 4 — Upper bound on s
There is no (186, m, 576)-net in base 4 for arbitrarily large m, because
- m-reduction [i] would yield (186, 2874, 576)-net in base 4, but
- extracting embedded OOA [i] would yield OOA(42874, 576, S4, 5, 2688), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 695982 619342 570703 028630 348659 368037 299334 330893 273013 790912 612120 320395 363974 864384 187499 109749 762327 687041 350599 151809 956450 872918 147156 594769 714655 920024 260915 536045 585973 747199 743598 647268 717298 224524 298656 727162 696879 344693 369826 392305 957395 553301 906244 364635 003140 963638 649887 578921 146849 663948 838679 496051 723921 426431 165747 941627 728246 978345 478049 261844 689978 017392 562904 162211 457964 000968 042040 961216 899488 285033 965808 548428 749226 511345 314600 366013 775014 532019 890277 547297 213866 298905 611524 460524 517638 934229 596563 690691 086138 129374 669464 761271 594623 370226 761877 098701 294088 583007 705411 907899 848622 461835 432884 229943 132574 328160 699469 874158 633515 588742 731165 154949 834859 227485 523804 545422 051989 898162 270060 260329 429779 525288 232404 434091 822814 682702 774033 223745 560949 408069 811903 083075 582013 109574 588916 997792 080102 978145 853642 163667 074511 737034 851391 797203 527246 605666 165037 548081 907988 064263 362200 517537 361720 366852 349739 705920 497014 849411 141359 185399 604857 699807 974471 651240 576982 261996 609943 372357 092594 336160 117093 948831 516703 696874 066718 626039 098448 785714 044812 718302 490366 647076 549061 873243 134517 662331 860334 604924 499715 220635 228030 991552 153139 176305 410132 773579 339989 307120 063386 301774 798488 632693 467170 292448 809754 057334 139092 625446 891860 621256 549754 312122 911127 464442 265802 202412 841109 926235 030523 788760 363128 278097 514176 664482 052842 372776 193374 172802 002519 868132 659877 497233 913975 261726 051590 059279 896716 521144 644398 971656 402758 420630 072412 890229 269842 773716 217863 414341 986148 440523 843078 979927 160469 159590 486179 958638 840707 296326 551456 951357 819386 656943 982484 726265 753313 585165 080917 465564 188156 566172 090123 263585 876605 597497 887128 098521 784109 341252 105824 020142 884520 385246 145751 175099 180383 224141 578144 887412 359168 / 2689 > 42874 [i]
- extracting embedded OOA [i] would yield OOA(42874, 576, S4, 5, 2688), but