Best Known (60, 224, s)-Nets in Base 4
(60, 224, 66)-Net over F4 — Constructive and digital
Digital (60, 224, 66)-net over F4, using
- t-expansion [i] based on digital (49, 224, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(60, 224, 91)-Net over F4 — Digital
Digital (60, 224, 91)-net over F4, using
- t-expansion [i] based on digital (50, 224, 91)-net over F4, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 50 and N(F) ≥ 91, using
- net from sequence [i] based on digital (50, 90)-sequence over F4, using
(60, 224, 304)-Net over F4 — Upper bound on s (digital)
There is no digital (60, 224, 305)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(4224, 305, F4, 164) (dual of [305, 81, 165]-code), but
- residual code [i] would yield OA(460, 140, S4, 41), but
- the linear programming bound shows that M ≥ 879403 484026 313933 129107 893130 654952 488416 854359 107391 996054 021035 128392 974988 409099 175067 144881 999812 150052 449544 895148 851200 / 619301 085252 374849 001693 023953 651889 253595 081048 920563 530321 558861 109148 317743 673454 318139 > 460 [i]
- residual code [i] would yield OA(460, 140, S4, 41), but
(60, 224, 396)-Net in Base 4 — Upper bound on s
There is no (60, 224, 397)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 782 207410 176552 603945 846226 685758 966655 345644 078443 299545 071823 040201 793758 783750 619125 669496 887800 008482 953944 658533 931562 467311 877840 > 4224 [i]