Best Known (52, 146, s)-Nets in Base 3
(52, 146, 48)-Net over F3 — Constructive and digital
Digital (52, 146, 48)-net over F3, using
- t-expansion [i] based on digital (45, 146, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(52, 146, 64)-Net over F3 — Digital
Digital (52, 146, 64)-net over F3, using
- t-expansion [i] based on digital (49, 146, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(52, 146, 215)-Net over F3 — Upper bound on s (digital)
There is no digital (52, 146, 216)-net over F3, because
- 1 times m-reduction [i] would yield digital (52, 145, 216)-net over F3, but
- extracting embedded orthogonal array [i] would yield linear OA(3145, 216, F3, 93) (dual of [216, 71, 94]-code), but
- residual code [i] would yield OA(352, 122, S3, 31), but
- the linear programming bound shows that M ≥ 19725 986797 755777 852323 435596 460479 202036 641392 776622 387026 170595 661601 866699 763499 067224 083319 101071 843283 443846 889719 591360 / 2985 345408 219380 711117 519513 518083 267277 757151 882703 066172 010819 020295 476643 056764 180222 169772 636319 > 352 [i]
- residual code [i] would yield OA(352, 122, S3, 31), but
- extracting embedded orthogonal array [i] would yield linear OA(3145, 216, F3, 93) (dual of [216, 71, 94]-code), but
(52, 146, 235)-Net in Base 3 — Upper bound on s
There is no (52, 146, 236)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 5230 332246 051100 618449 734558 979447 929621 190764 262077 492732 338819 830801 > 3146 [i]