Best Known (104, 131, s)-Nets in Base 2
(104, 131, 196)-Net over F2 — Constructive and digital
Digital (104, 131, 196)-net over F2, using
- 1 times m-reduction [i] based on digital (104, 132, 196)-net over F2, using
- trace code for nets [i] based on digital (5, 33, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- trace code for nets [i] based on digital (5, 33, 49)-net over F16, using
(104, 131, 374)-Net over F2 — Digital
Digital (104, 131, 374)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2131, 374, F2, 2, 27) (dual of [(374, 2), 617, 28]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2131, 512, F2, 2, 27) (dual of [(512, 2), 893, 28]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2131, 1024, F2, 27) (dual of [1024, 893, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- OOA 2-folding [i] based on linear OA(2131, 1024, F2, 27) (dual of [1024, 893, 28]-code), using
- discarding factors / shortening the dual code based on linear OOA(2131, 512, F2, 2, 27) (dual of [(512, 2), 893, 28]-NRT-code), using
(104, 131, 5784)-Net in Base 2 — Upper bound on s
There is no (104, 131, 5785)-net in base 2, because
- 1 times m-reduction [i] would yield (104, 130, 5785)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 1361 910797 431663 438719 452405 762978 703688 > 2130 [i]