Best Known (25, 25+11, s)-Nets in Base 2
(25, 25+11, 52)-Net over F2 — Constructive and digital
Digital (25, 36, 52)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (6, 11, 26)-net over F2, using
- digital (14, 25, 26)-net over F2, using
- 1 times m-reduction [i] based on digital (14, 26, 26)-net over F2, using
(25, 25+11, 62)-Net over F2 — Digital
Digital (25, 36, 62)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 62, F2, 2, 11) (dual of [(62, 2), 88, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(236, 64, F2, 2, 11) (dual of [(64, 2), 92, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OA(236, 128, F2, 11) (dual of [128, 92, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- OOA 2-folding [i] based on linear OA(236, 128, F2, 11) (dual of [128, 92, 12]-code), using
- discarding factors / shortening the dual code based on linear OOA(236, 64, F2, 2, 11) (dual of [(64, 2), 92, 12]-NRT-code), using
(25, 25+11, 326)-Net in Base 2 — Upper bound on s
There is no (25, 36, 327)-net in base 2, because
- 1 times m-reduction [i] would yield (25, 35, 327)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 34605 542252 > 235 [i]