Best Known (21, ∞, s)-Nets in Base 49
(21, ∞, 344)-Net over F49 — Constructive and digital
Digital (21, m, 344)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
(21, ∞, 1100)-Net in Base 49 — Upper bound on s
There is no (21, m, 1101)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (21, 1099, 1101)-net in base 49, but
- extracting embedded OOA [i] would yield OA(491099, 1101, S49, 1078), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 3 779339 159026 891077 659015 803035 683332 435498 155937 666607 073116 789351 988590 320364 740454 127407 307500 720857 078803 544424 264539 208726 290319 367302 039768 259299 812694 084348 027878 700759 863308 396224 903749 721285 106898 207232 135269 310826 530010 436574 881158 563456 555506 803053 047569 248489 461040 491838 277786 724943 495888 324309 671413 595709 782581 524191 993676 975583 453610 507271 389442 321439 171839 000935 263146 056599 471396 332019 636306 015143 778029 971345 600733 549839 996328 633056 898820 155075 700851 760995 840800 699733 649018 093587 674099 690568 060350 472777 005460 383390 756142 982589 256596 136019 593449 179192 396974 321584 319902 281743 674754 995468 950225 739184 301853 199687 931556 102257 568509 472574 282130 948743 496575 273373 633478 701910 517302 278092 814334 596600 743548 126943 052006 435076 228835 838700 163608 126597 431405 920700 311359 277831 683492 208435 653446 164724 143922 817025 008102 894316 779825 245843 972963 592733 704017 511267 745738 461390 379846 109291 666453 153207 342215 567023 364687 880880 364625 505697 544034 989456 157041 909582 217296 990713 440687 046128 651414 591901 401484 506158 059245 731132 931936 050279 206675 503411 602837 857430 462020 361588 848464 856675 909805 596989 307769 869034 871004 653095 308993 503411 906044 258123 328320 255163 327584 935954 337513 309908 805662 615776 208109 013371 697658 656533 481231 161417 981967 395405 418879 874594 077198 367455 159461 335097 074178 155910 740657 627387 752142 150122 144132 175665 818432 584493 172488 052560 934705 521501 528175 910266 137470 910985 640565 410489 266984 266595 787254 548944 911560 884010 183830 967262 729292 930442 604900 055609 051962 613786 749941 029020 182978 112970 852408 579862 686619 661728 918058 376234 929279 758840 489185 182611 333238 326428 201646 268152 426782 053901 475938 433968 732352 430694 294050 452247 106946 871175 205870 955363 635280 272573 865391 295474 259033 511825 401616 141761 661469 242916 930399 476958 097371 965937 683460 152709 670409 615499 472327 230946 150703 495062 148271 861911 343151 651681 365652 196413 520262 621270 335723 092398 360023 / 1079 > 491099 [i]
- extracting embedded OOA [i] would yield OA(491099, 1101, S49, 1078), but