Best Known (74−56, 74, s)-Nets in Base 5
(74−56, 74, 43)-Net over F5 — Constructive and digital
Digital (18, 74, 43)-net over F5, using
- net from sequence [i] based on digital (18, 42)-sequence over F5, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F5 with g(F) = 17, N(F) = 42, and 1 place with degree 2 [i] based on function field F/F5 with g(F) = 17 and N(F) ≥ 42, using an explicitly constructive algebraic function field [i]
(74−56, 74, 134)-Net in Base 5 — Upper bound on s
There is no (18, 74, 135)-net in base 5, because
- extracting embedded orthogonal array [i] would yield OA(574, 135, S5, 56), but
- the linear programming bound shows that M ≥ 43 927254 602685 604737 769780 050389 651290 584745 415425 419630 252656 117199 331192 606529 622677 758816 021272 934360 065742 209285 161127 391793 049330 517566 383735 737284 043460 068458 326081 730248 106860 768630 976821 214062 510989 606380 462646 484375 / 7558 387585 900587 374093 050456 176553 314572 659729 483567 414755 400109 448517 687247 745169 534721 500940 816391 332250 353462 202806 967039 291828 856673 812128 888296 596368 868907 636850 628887 > 574 [i]