Best Known (124, 124+8, s)-Nets in Base 2
(124, 124+8, 4194558)-Net over F2 — Constructive and digital
Digital (124, 132, 4194558)-net over F2, using
- t-expansion [i] based on digital (123, 132, 4194558)-net over F2, using
- net defined by OOA [i] based on linear OOA(2132, 4194558, F2, 9, 9) (dual of [(4194558, 9), 37750890, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2132, 4194558, F2, 8, 9) (dual of [(4194558, 8), 33556332, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(216, 257, F2, 8, 4) (dual of [(257, 8), 2040, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(216, 257, F2, 4, 4) (dual of [(257, 4), 1012, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(216, 257, F2, 3, 4) (dual of [(257, 3), 755, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (12, 16, 257)-net over F2, using
- appending kth column [i] based on linear OOA(216, 257, F2, 3, 4) (dual of [(257, 3), 755, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(216, 257, F2, 4, 4) (dual of [(257, 4), 1012, 5]-NRT-code), using
- 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(216, 257, F2, 8, 4) (dual of [(257, 8), 2040, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2132, 4194558, F2, 8, 9) (dual of [(4194558, 8), 33556332, 10]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2132, 4194558, F2, 9, 9) (dual of [(4194558, 9), 37750890, 10]-NRT-code), using
(124, 124+8, large)-Net over F2 — Digital
Digital (124, 132, large)-net over F2, using
- 215 times duplication [i] based on digital (109, 117, large)-net over F2, using
- t-expansion [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
- t-expansion [i] based on digital (108, 117, large)-net over F2, using
(124, 124+8, large)-Net in Base 2 — Upper bound on s
There is no (124, 132, large)-net in base 2, because
- 6 times m-reduction [i] would yield (124, 126, large)-net in base 2, but