Best Known (50, ∞, s)-Nets in Base 3
(50, ∞, 48)-Net over F3 — Constructive and digital
Digital (50, m, 48)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (50, 47)-sequence over F3, using
- t-expansion [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
- t-expansion [i] based on digital (45, 47)-sequence over F3, using
(50, ∞, 64)-Net over F3 — Digital
Digital (50, m, 64)-net over F3 for arbitrarily large m, using
- net from sequence [i] based on digital (50, 63)-sequence over F3, using
- t-expansion [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
- t-expansion [i] based on digital (49, 63)-sequence over F3, using
(50, ∞, 111)-Net in Base 3 — Upper bound on s
There is no (50, m, 112)-net in base 3 for arbitrarily large m, because
- m-reduction [i] would yield (50, 554, 112)-net in base 3, but
- extracting embedded OOA [i] would yield OOA(3554, 112, S3, 5, 504), but
- the (dual) Plotkin bound for OOAs shows that M ≥ 1186 145528 364117 535737 037647 785197 557137 685959 372186 469530 968081 490221 223844 563942 363921 609990 826865 796813 560521 588061 834264 622037 072704 491910 984592 526076 703801 733360 115161 336227 325282 271920 754570 543993 276437 453515 047928 856365 953996 034966 307116 714278 332445 634035 374809 / 505 > 3554 [i]
- extracting embedded OOA [i] would yield OOA(3554, 112, S3, 5, 504), but