Best Known (136, 136+∞, s)-Nets in Base 5
(136, 136+∞, 117)-Net over F5 — Constructive and digital
Digital (136, m, 117)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (136, 116)-sequence over F5, using
- base reduction for sequences [i] based on digital (10, 116)-sequence over F25, using
- s-reduction based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- s-reduction based on digital (10, 125)-sequence over F25, using
- base reduction for sequences [i] based on digital (10, 116)-sequence over F25, using
(136, 136+∞, 210)-Net over F5 — Digital
Digital (136, m, 210)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (136, 209)-sequence over F5, using
- t-expansion [i] based on digital (127, 209)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 127 and N(F) ≥ 210, using
- t-expansion [i] based on digital (127, 209)-sequence over F5, using
(136, 136+∞, 563)-Net in Base 5 — Upper bound on s
There is no (136, m, 564)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (136, 2251, 564)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(52251, 564, S5, 4, 2115), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 14562 473062 937334 562959 880846 736529 626678 071104 906853 297055 203438 983206 931358 145606 406349 750172 682158 653148 830322 710294 073658 599626 985939 407746 794652 830024 508781 710007 263541 585929 364400 234738 600163 617174 230344 040669 158716 676386 424533 802079 498728 303508 957838 446613 071388 642803 593161 388389 672094 414578 478336 955989 878069 432173 227291 432519 536035 936682 884533 181931 425707 997645 456949 580718 201087 469062 804535 088190 610261 970343 907319 507743 790250 381981 173472 675950 529087 192493 033056 608511 142536 057264 680349 359936 135636 035190 587163 105809 696741 443663 654167 445869 093209 807979 789231 601599 986140 635328 976012 817100 303342 091299 071613 939356 523709 496638 833480 472520 407150 006183 901176 182918 647212 645613 976545 919214 619705 522745 421163 508000 625767 798025 675440 765053 102352 264368 978844 029255 892238 572404 732039 848270 340389 292829 800636 364845 369256 690671 910292 485348 290658 112463 857812 239548 889979 571978 792651 021663 087179 232726 151229 089477 790278 308900 875235 394161 575959 782678 536087 464548 771780 938621 294848 716431 408924 751833 526848 171988 509289 702597 573745 604717 100243 164558 862765 697187 442726 653453 473150 516297 777068 722572 756690 433828 377242 429293 111100 652409 890463 996753 068645 619201 000065 603613 747508 266472 691398 004126 514668 744155 536724 141279 481071 765967 144168 565427 561080 275240 401150 523675 412493 943889 695849 554358 415045 941703 711680 885881 999540 333893 318413 284963 121911 597572 499054 545021 418941 745728 622808 739439 228362 450212 354204 316956 787200 006995 059330 781921 874048 443572 190261 165288 287759 610486 579400 662307 434563 348990 721718 584244 451469 085021 297843 039584 632893 507936 714228 012675 675927 312113 344669 342041 015625 / 529 > 52251 [i]
- extracting embedded OOA [i] would yield OOA(52251, 564, S5, 4, 2115), but