Best Known (19, ∞, s)-Nets in Base 49
(19, ∞, 96)-Net over F49 — Constructive and digital
Digital (19, m, 96)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (19, 95)-sequence over F49, using
- t-expansion [i] based on digital (17, 95)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) ≤ 17 and N(F) ≥ 96, using
- F4 from the tower of function fields by GarcÃa, Stichtenoth, and Rück over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) ≤ 17 and N(F) ≥ 96, using
- t-expansion [i] based on digital (17, 95)-sequence over F49, using
(19, ∞, 1000)-Net in Base 49 — Upper bound on s
There is no (19, m, 1001)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (19, 999, 1001)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49999, 1001, S49, 980), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 109945 654393 271347 635391 812258 621049 334622 122767 803823 440374 309949 249516 538205 984827 879004 008468 409398 649711 983718 841193 202616 601484 569474 524598 900199 045954 259347 307466 490945 256630 330388 063515 067706 373202 007973 467153 874398 620319 673524 188165 379843 410179 241181 245914 256426 204845 025059 421038 170627 682352 652633 362657 182329 784937 089420 494892 885191 598154 384278 436700 875826 362802 037527 594970 346685 084812 366006 889623 832158 460727 038852 524366 296404 053652 387943 997495 656482 503252 405196 357517 524376 609427 811131 641951 929197 192719 648863 211811 408473 679703 558172 628976 130769 831238 307638 023818 279387 082420 157588 360778 020629 570499 121870 809990 514589 313768 111158 710803 588658 651495 870178 785150 228874 747595 293849 898936 829280 835464 029241 059509 055914 489526 822503 255094 185676 681775 489638 555795 172251 283214 337152 810841 654220 776817 821618 834069 135477 405126 919643 944793 373728 444031 201570 445181 511896 469546 960837 487946 624996 677279 591292 477091 971729 912035 400603 596367 555894 672901 364513 581165 687462 869219 638158 458290 160001 584025 906485 156188 224605 063195 798346 746035 049971 375189 240943 296046 674418 916163 876666 893428 861233 882352 173616 287149 211241 703028 103897 131946 267824 061582 757566 800354 692860 665950 223041 236662 412258 479403 995038 804252 918487 262446 994621 355326 158422 565702 501233 456946 308598 366370 222159 043031 428500 628081 688204 402544 969254 275871 553288 420126 574798 026896 203615 318567 534548 994514 429816 121114 081510 798418 937207 728307 554894 441876 581175 902900 797700 056351 536375 353910 941719 044781 499731 383319 815198 459008 093036 273008 302574 197294 409173 357568 287677 370609 990456 389979 343427 941161 137620 417461 052052 511915 689190 375025 130429 827019 577426 865199 497606 428526 660930 547687 690447 226946 318872 808240 400621 733740 275973 988462 757928 400007 / 327 > 49999 [i]
- extracting embedded OOA [i] would yield OA(49999, 1001, S49, 980), but