Best Known (52−32, 52, s)-Nets in Base 3
(52−32, 52, 28)-Net over F3 — Constructive and digital
Digital (20, 52, 28)-net over F3, using
- t-expansion [i] based on digital (15, 52, 28)-net over F3, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 15 and N(F) ≥ 28, using
- net from sequence [i] based on digital (15, 27)-sequence over F3, using
(52−32, 52, 32)-Net over F3 — Digital
Digital (20, 52, 32)-net over F3, using
- t-expansion [i] based on digital (19, 52, 32)-net over F3, using
- net from sequence [i] based on digital (19, 31)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 19 and N(F) ≥ 32, using
- net from sequence [i] based on digital (19, 31)-sequence over F3, using
(52−32, 52, 104)-Net in Base 3 — Upper bound on s
There is no (20, 52, 105)-net in base 3, because
- extracting embedded orthogonal array [i] would yield OA(352, 105, S3, 32), but
- the linear programming bound shows that M ≥ 29 330225 592130 803136 745611 225395 212262 193588 634831 271757 335853 509826 810148 464776 801448 991899 388366 356985 499477 294420 691377 937257 862478 653455 313397 755257 162480 466860 126870 987226 968820 627089 194046 / 4 200617 664767 811156 493569 334999 400989 114272 802755 402230 840938 949130 567633 580649 943699 209510 278255 358909 727860 736080 753000 241068 211059 029487 882457 532813 925399 388366 987623 > 352 [i]