Best Known (162, 248, s)-Nets in Base 4
(162, 248, 200)-Net over F4 — Constructive and digital
Digital (162, 248, 200)-net over F4, using
- t-expansion [i] based on digital (161, 248, 200)-net over F4, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the 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) = 161 and N(F) ≥ 200, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
(162, 248, 240)-Net in Base 4 — Constructive
(162, 248, 240)-net in base 4, using
- t-expansion [i] based on (161, 248, 240)-net in base 4, using
- 2 times m-reduction [i] based on (161, 250, 240)-net in base 4, using
- trace code for nets [i] based on (36, 125, 120)-net in base 16, using
- base change [i] based on digital (11, 100, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 100, 120)-net over F32, using
- trace code for nets [i] based on (36, 125, 120)-net in base 16, using
- 2 times m-reduction [i] based on (161, 250, 240)-net in base 4, using
(162, 248, 578)-Net over F4 — Digital
Digital (162, 248, 578)-net over F4, using
(162, 248, 16663)-Net in Base 4 — Upper bound on s
There is no (162, 248, 16664)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 204690 664303 366437 666771 530574 745047 708574 574939 931556 593288 178249 430071 825115 124713 021548 297242 000867 017670 776847 420733 831262 589909 346398 945451 698160 > 4248 [i]