Best Known (202−144, 202, s)-Nets in Base 4
(202−144, 202, 66)-Net over F4 — Constructive and digital
Digital (58, 202, 66)-net over F4, using
- t-expansion [i] based on digital (49, 202, 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
(202−144, 202, 91)-Net over F4 — Digital
Digital (58, 202, 91)-net over F4, using
- t-expansion [i] based on digital (50, 202, 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
(202−144, 202, 357)-Net over F4 — Upper bound on s (digital)
There is no digital (58, 202, 358)-net over F4, because
- extracting embedded orthogonal array [i] would yield linear OA(4202, 358, F4, 144) (dual of [358, 156, 145]-code), but
- residual code [i] would yield OA(458, 213, S4, 36), but
- the linear programming bound shows that M ≥ 7 866958 687285 876635 384332 274577 437607 350342 946368 588838 836611 539357 984012 369920 / 88 856238 935032 449112 554626 779870 493844 853867 > 458 [i]
- residual code [i] would yield OA(458, 213, S4, 36), but
(202−144, 202, 393)-Net in Base 4 — Upper bound on s
There is no (58, 202, 394)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 44 176468 826956 372226 063154 688336 026855 587329 197193 658178 694184 608151 113806 116344 344373 837135 457779 323885 533487 713189 000770 > 4202 [i]