Best Known (18, 18+∞, s)-Nets in Base 49
(18, 18+∞, 96)-Net over F49 — Constructive and digital
Digital (18, m, 96)-net over F49 for arbitrarily large m, using
- net from sequence [i] based on digital (18, 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
(18, 18+∞, 950)-Net in Base 49 — Upper bound on s
There is no (18, m, 951)-net in base 49 for arbitrarily large m, because
- m-reduction [i] would yield (18, 949, 951)-net in base 49, but
- extracting embedded OOA [i] would yield OA(49949, 951, S49, 931), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 24279 851792 777102 533487 630540 820952 479622 803854 754383 569392 034266 569175 977853 976965 341025 503315 803387 786199 885601 920661 782119 110744 035984 165933 996148 909792 219709 189600 917147 885824 572323 082798 851998 665111 230752 990061 390186 495371 505704 271771 204958 220255 184049 207262 180753 728838 593528 965331 734209 986533 053803 772596 593438 483011 609985 812100 103129 693566 058994 205404 337558 491555 857484 346600 836144 325778 608022 818515 784463 454444 104682 536796 867620 670505 418453 127109 541918 221306 634824 600108 925146 493151 033105 979921 257096 566487 094019 052118 558932 577264 429474 840092 008689 152081 728202 742023 162651 491974 255308 535756 623781 546957 218444 299724 427666 140184 916311 764934 912707 829952 507044 442042 487600 545513 658052 193732 078773 006065 994899 202490 686174 408419 227862 318597 695814 847607 406330 776077 518535 467528 000932 686370 454695 959026 026834 779397 125969 652320 817745 817700 802291 319847 694140 176502 411158 542220 323906 681732 136230 380726 852547 103949 757554 264002 444856 650813 429355 162899 565942 765976 981081 114166 016372 388169 428545 865039 167300 937315 592774 721308 585053 229456 514013 502573 477640 873681 476140 303420 313961 835823 584578 986160 633513 877893 964721 423504 437072 647325 377236 407446 132668 274339 278413 975598 148495 990775 017041 955331 610441 798214 794740 920770 801462 574223 975304 797224 772217 965331 520072 549299 891423 525336 635960 493260 917484 193138 375896 321689 906836 217343 031326 474172 803344 417743 358226 623525 020904 938219 655098 815478 526266 172781 342317 205354 226470 162123 363321 013278 704703 696003 299294 447860 958801 043346 936490 950608 876079 352525 425243 502345 090246 169319 335745 897757 266677 057124 164985 215549 029771 553224 884741 756121 371226 808166 501588 204321 386165 700005 / 233 > 49949 [i]
- extracting embedded OOA [i] would yield OA(49949, 951, S49, 931), but