Best Known (128, 128+11, s)-Nets in Base 2
(128, 128+11, 2796200)-Net over F2 — Constructive and digital
Digital (128, 139, 2796200)-net over F2, using
- net defined by OOA [i] based on linear OOA(2139, 2796200, F2, 14, 11) (dual of [(2796200, 14), 39146661, 12]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2139, 8388601, F2, 2, 11) (dual of [(8388601, 2), 16777063, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2139, large, F2, 2, 11), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2139, 8388601, F2, 2, 11) (dual of [(8388601, 2), 16777063, 12]-NRT-code), using
(128, 128+11, 4194301)-Net over F2 — Digital
Digital (128, 139, 4194301)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2139, 4194301, F2, 4, 11) (dual of [(4194301, 4), 16777065, 12]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2139, 8388602, F2, 2, 11) (dual of [(8388602, 2), 16777065, 12]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2139, large, F2, 2, 11), using
- OOA 2-folding [i] based on linear OOA(2139, 8388602, F2, 2, 11) (dual of [(8388602, 2), 16777065, 12]-NRT-code), using
(128, 128+11, large)-Net in Base 2 — Upper bound on s
There is no (128, 139, large)-net in base 2, because
- 9 times m-reduction [i] would yield (128, 130, large)-net in base 2, but