Best Known (111, 111+9, s)-Nets in Base 2
(111, 111+9, 4194304)-Net over F2 — Constructive and digital
Digital (111, 120, 4194304)-net over F2, using
- net defined by OOA [i] based on linear OOA(2120, 4194304, F2, 9, 9) (dual of [(4194304, 9), 37748616, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2120, 4194304, F2, 8, 9) (dual of [(4194304, 8), 33554312, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(24, 3, F2, 8, 4) (dual of [(3, 8), 20, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(8;20,2) [i]
- linear OOA(2116, 4194301, F2, 8, 9) (dual of [(4194301, 8), 33554292, 10]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2116, large, F2, 2, 9), using
- linear OOA(24, 3, F2, 8, 4) (dual of [(3, 8), 20, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2120, 4194304, F2, 8, 9) (dual of [(4194304, 8), 33554312, 10]-NRT-code), using
(111, 111+9, large)-Net over F2 — Digital
Digital (111, 120, large)-net over F2, using
- 23 times duplication [i] based on digital (108, 117, large)-net over F2, using
- net defined by OOA [i] based on linear OOA(2117, large, F2, 9, 9), using
- appending kth column [i] based on linear OOA(2117, large, F2, 8, 9), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2117, large, F2, 3, 9), using
- appending kth column [i] based on linear OOA(2117, large, F2, 8, 9), using
- net defined by OOA [i] based on linear OOA(2117, large, F2, 9, 9), using
(111, 111+9, large)-Net in Base 2 — Upper bound on s
There is no (111, 120, large)-net in base 2, because
- 7 times m-reduction [i] would yield (111, 113, large)-net in base 2, but