Best Known (132, 132+68, s)-Nets in Base 4
(132, 132+68, 163)-Net over F4 — Constructive and digital
Digital (132, 200, 163)-net over F4, using
- 2 times m-reduction [i] based on digital (132, 202, 163)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (15, 50, 33)-net over F4, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 15 and N(F) ≥ 33, using
- net from sequence [i] based on digital (15, 32)-sequence over F4, using
- digital (82, 152, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 76, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 76, 65)-net over F16, using
- digital (15, 50, 33)-net over F4, using
- (u, u+v)-construction [i] based on
(132, 132+68, 240)-Net in Base 4 — Constructive
(132, 200, 240)-net in base 4, using
- t-expansion [i] based on (131, 200, 240)-net in base 4, using
- trace code for nets [i] based on (31, 100, 120)-net in base 16, using
- base change [i] based on digital (11, 80, 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, 80, 120)-net over F32, using
- trace code for nets [i] based on (31, 100, 120)-net in base 16, using
(132, 132+68, 512)-Net over F4 — Digital
Digital (132, 200, 512)-net over F4, using
(132, 132+68, 15671)-Net in Base 4 — Upper bound on s
There is no (132, 200, 15672)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2 584471 116958 124624 816779 793218 368872 711398 225450 921569 038904 035939 420220 881935 229822 334310 702423 833000 559137 283373 558083 > 4200 [i]