Best Known (74−45, 74, s)-Nets in Base 3
(74−45, 74, 37)-Net over F3 — Constructive and digital
Digital (29, 74, 37)-net over F3, using
- t-expansion [i] based on digital (27, 74, 37)-net over F3, using
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
- Niederreiter–Xing sequence construction III based on the algebraic function field F/F3 with g(F) = 26, N(F) = 36, and 1 place with degree 2 [i] based on function field F/F3 with g(F) = 26 and N(F) ≥ 36, using an explicitly constructive algebraic function field [i]
- net from sequence [i] based on digital (27, 36)-sequence over F3, using
(74−45, 74, 42)-Net over F3 — Digital
Digital (29, 74, 42)-net over F3, using
- net from sequence [i] based on digital (29, 41)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 29 and N(F) ≥ 42, using
(74−45, 74, 134)-Net in Base 3 — Upper bound on s
There is no (29, 74, 135)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(374, 135, S3, 45), but
- the linear programming bound shows that M ≥ 3149 102978 502159 702832 324850 000724 343690 781397 590391 301020 103565 627253 799681 342733 232096 935540 172381 288036 145917 424600 949572 865273 314090 681217 849098 897411 221037 317415 036463 486694 956203 154705 978691 418966 997838 451810 319831 790028 969021 194326 831692 990368 995587 851882 061731 / 14597 778493 990865 194663 196016 206641 110192 731698 087051 433957 071155 012610 160359 950448 727704 848834 991243 819836 175998 265310 906935 374233 433468 848031 172344 125058 682610 464451 658601 633589 335287 574794 198669 581670 459179 939879 334859 216869 016355 > 374 [i]