Best Known (202−147, 202, s)-Nets in Base 4
(202−147, 202, 66)-Net over F4 — Constructive and digital
Digital (55, 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
(202−147, 202, 91)-Net over F4 — Digital
Digital (55, 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
(202−147, 202, 308)-Net over F4 — Upper bound on s (digital)
There is no digital (55, 202, 309)-net over F4, because
- 3 times m-reduction [i] would yield digital (55, 199, 309)-net over F4, but
- extracting embedded orthogonal array [i] would yield linear OA(4199, 309, F4, 144) (dual of [309, 110, 145]-code), but
- residual code [i] would yield OA(455, 164, S4, 36), but
- the linear programming bound shows that M ≥ 980 201801 606598 702017 212850 515741 792418 086779 414793 869747 648944 529897 580134 400000 / 752717 700220 343776 849584 966340 992475 812762 611911 > 455 [i]
- residual code [i] would yield OA(455, 164, S4, 36), but
- extracting embedded orthogonal array [i] would yield linear OA(4199, 309, F4, 144) (dual of [309, 110, 145]-code), but
(202−147, 202, 367)-Net in Base 4 — Upper bound on s
There is no (55, 202, 368)-net in base 4, because
- 1 times m-reduction [i] would yield (55, 201, 368)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 11 844400 361799 199731 322165 371226 454919 361233 215340 308131 547739 574352 360878 463277 081225 898806 106871 328263 777733 815495 730325 > 4201 [i]