Best Known (154−99, 154, s)-Nets in Base 3
(154−99, 154, 48)-Net over F3 — Constructive and digital
Digital (55, 154, 48)-net over F3, using
- t-expansion [i] based on digital (45, 154, 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
(154−99, 154, 64)-Net over F3 — Digital
Digital (55, 154, 64)-net over F3, using
- t-expansion [i] based on digital (49, 154, 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
(154−99, 154, 222)-Net over F3 — Upper bound on s (digital)
There is no digital (55, 154, 223)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(3154, 223, F3, 99) (dual of [223, 69, 100]-code), but
- residual code [i] would yield OA(355, 123, S3, 33), but
- the linear programming bound shows that M ≥ 148 070708 119494 381097 768298 762064 420941 614688 018061 442730 314757 617739 382441 097813 300293 193176 549890 233732 442129 700432 638201 644702 914535 355721 641913 236632 545448 107728 196475 461463 715767 220573 162925 / 812684 026412 505193 891098 210421 866334 373415 292609 947732 124728 804133 321909 393097 168706 926460 978407 999004 611093 804726 375841 495072 336504 276946 318881 556551 454271 872053 611339 > 355 [i]
- residual code [i] would yield OA(355, 123, S3, 33), but
(154−99, 154, 249)-Net in Base 3 — Upper bound on s
There is no (55, 154, 250)-net in base 3, because
- 1 times m-reduction [i] would yield (55, 153, 250)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 10 472571 986212 094490 567229 716819 754614 263581 059276 221319 205729 521703 584021 > 3153 [i]