Best Known (163, 249, s)-Nets in Base 4
(163, 249, 200)-Net over F4 — Constructive and digital
Digital (163, 249, 200)-net over F4, using
- t-expansion [i] based on digital (161, 249, 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
(163, 249, 240)-Net in Base 4 — Constructive
(163, 249, 240)-net in base 4, using
- t-expansion [i] based on (161, 249, 240)-net in base 4, using
- 1 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
- 1 times m-reduction [i] based on (161, 250, 240)-net in base 4, using
(163, 249, 588)-Net over F4 — Digital
Digital (163, 249, 588)-net over F4, using
(163, 249, 17210)-Net in Base 4 — Upper bound on s
There is no (163, 249, 17211)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 818462 228840 404151 897238 970828 901743 224426 159125 157215 725029 697262 047907 464250 528916 831377 754643 461544 955963 078934 584508 391540 044988 815759 089461 851100 > 4249 [i]