Best Known (74, 74+∞, s)-Nets in Base 5
(74, 74+∞, 82)-Net over F5 — Constructive and digital
Digital (74, m, 82)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (74, 81)-sequence over F5, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 48 and N(F) ≥ 82, using
- t-expansion [i] based on digital (48, 81)-sequence over F5, using
(74, 74+∞, 132)-Net over F5 — Digital
Digital (74, m, 132)-net over F5 for arbitrarily large m, using
- net from sequence [i] based on digital (74, 131)-sequence over F5, using
- t-expansion [i] based on digital (67, 131)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 67 and N(F) ≥ 132, using
- t-expansion [i] based on digital (67, 131)-sequence over F5, using
(74, 74+∞, 314)-Net in Base 5 — Upper bound on s
There is no (74, m, 315)-net in base 5 for arbitrarily large m, because
- m-reduction [i] would yield (74, 1255, 315)-net in base 5, but
- extracting embedded OOA [i] would yield OOA(51255, 315, S5, 4, 1181), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 5238 884245 225251 908204 325972 583367 044101 343203 682888 232064 875191 953101 422099 770624 386567 528852 479793 638013 497960 169893 444382 591418 807367 122333 063511 120823 442805 952613 895391 805804 806783 833522 506938 114579 692787 444854 446243 782651 862968 572271 370858 928004 408223 312371 525527 506241 307460 916163 061215 253941 314883 347680 103492 100456 603906 360150 499747 871932 671232 849416 175507 672353 014709 387890 919050 142687 578641 929753 253867 472285 587481 254875 773066 612011 674350 638899 605376 842044 636399 504064 173466 943345 069684 136232 167083 005378 473320 641759 085099 431099 107584 120751 013276 186370 264835 496665 802010 657664 543851 462334 495925 714470 143703 557072 728908 545835 243393 470803 566214 406533 349824 920542 863168 474398 111176 050088 308763 871183 883547 219062 731843 024004 479643 788519 073031 189996 255416 999666 611111 445820 368504 631105 303002 326550 695022 631073 129722 900812 033445 309815 783696 993918 283624 225296 080112 457275 390625 / 197 > 51255 [i]
- extracting embedded OOA [i] would yield OOA(51255, 315, S5, 4, 1181), but