Best Known (226−47, 226, s)-Nets in Base 2
(226−47, 226, 260)-Net over F2 — Constructive and digital
Digital (179, 226, 260)-net over F2, using
- t-expansion [i] based on digital (177, 226, 260)-net over F2, using
- 2 times m-reduction [i] based on digital (177, 228, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 57, 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, 57, 65)-net over F16, using
- 2 times m-reduction [i] based on digital (177, 228, 260)-net over F2, using
(226−47, 226, 512)-Net over F2 — Digital
Digital (179, 226, 512)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2226, 512, F2, 2, 47) (dual of [(512, 2), 798, 48]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2226, 1024, F2, 47) (dual of [1024, 798, 48]-code), using
- an extension Ce(46) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,46], and designed minimum distance d ≥ |I|+1 = 47 [i]
- OOA 2-folding [i] based on linear OA(2226, 1024, F2, 47) (dual of [1024, 798, 48]-code), using
(226−47, 226, 8270)-Net in Base 2 — Upper bound on s
There is no (179, 226, 8271)-net in base 2, because
- 1 times m-reduction [i] would yield (179, 225, 8271)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 53 981001 242598 023719 843047 109819 012183 883035 595353 612966 207174 208008 > 2225 [i]