Best Known (70−53, 70, s)-Nets in Base 5
(70−53, 70, 42)-Net over F5 — Constructive and digital
Digital (17, 70, 42)-net over F5, using
- net from sequence [i] based on digital (17, 41)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using
(70−53, 70, 131)-Net in Base 5 — Upper bound on s
There is no (17, 70, 132)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(570, 132, S5, 53), but
- the linear programming bound shows that M ≥ 484 334401 119410 783555 749940 842394 005937 447155 228732 126229 608693 161906 940228 597216 475643 127860 880467 484319 064937 903983 748418 615852 968627 901966 430510 130587 336527 841533 725686 992001 264741 137664 419516 999634 619802 694857 071401 202119 886875 152587 890625 / 51 634906 738874 227956 798813 433740 491314 129593 248133 302427 482101 849119 434105 537479 371503 343612 264357 650495 768934 423538 549329 333663 516888 984294 208243 492116 213821 196876 117738 840327 435947 663286 477813 > 570 [i]