Best Known (128, 161, s)-Nets in Base 2
(128, 161, 260)-Net over F2 — Constructive and digital
Digital (128, 161, 260)-net over F2, using
- 21 times duplication [i] based on digital (127, 160, 260)-net over F2, using
- t-expansion [i] based on digital (126, 160, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 40, 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, 40, 65)-net over F16, using
- t-expansion [i] based on digital (126, 160, 260)-net over F2, using
(128, 161, 433)-Net over F2 — Digital
Digital (128, 161, 433)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2161, 433, F2, 2, 33) (dual of [(433, 2), 705, 34]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2161, 512, F2, 2, 33) (dual of [(512, 2), 863, 34]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2161, 1024, F2, 33) (dual of [1024, 863, 34]-code), using
- an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- OOA 2-folding [i] based on linear OA(2161, 1024, F2, 33) (dual of [1024, 863, 34]-code), using
- discarding factors / shortening the dual code based on linear OOA(2161, 512, F2, 2, 33) (dual of [(512, 2), 863, 34]-NRT-code), using
(128, 161, 6940)-Net in Base 2 — Upper bound on s
There is no (128, 161, 6941)-net in base 2, because
- 1 times m-reduction [i] would yield (128, 160, 6941)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1 464143 534032 915068 416152 663977 451301 912682 871851 > 2160 [i]