Best Known (169−11, 169, s)-Nets in Base 2
(169−11, 169, 4202494)-Net over F2 — Constructive and digital
Digital (158, 169, 4202494)-net over F2, using
- 21 times duplication [i] based on digital (157, 168, 4202494)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (23, 28, 8193)-net over F2, using
- digital (129, 140, 4194301)-net over F2, using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2140, large, F2, 3, 11), using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- (u, u+v)-construction [i] based on
(169−11, 169, 4202500)-Net in Base 2 — Constructive
(158, 169, 4202500)-net in base 2, using
- (u, u+v)-construction [i] based on
- (24, 29, 8199)-net in base 2, using
- net defined by OOA [i] based on OOA(229, 8199, S2, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(229, 16399, S2, 5), using
- construction X4 applied to RM(1,14) ⊂ K(14) [i] based on
- OA(228, 16384, S2, 5), using Kerdock OA K(14) [i]
- linear OA(215, 16384, F2, 3) (dual of [16384, 16369, 4]-code or 16384-cap in PG(14,2)), using Reed–Muller code RM(1,14) [i]
- linear OA(214, 15, F2, 13) (dual of [15, 1, 14]-code), using
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- dual of repetition code with length 15 [i]
- strength reduction [i] based on linear OA(214, 15, F2, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,2)), using
- linear OA(21, 15, F2, 1) (dual of [15, 14, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to RM(1,14) ⊂ K(14) [i] based on
- OOA 2-folding and stacking with additional row [i] based on OA(229, 16399, S2, 5), using
- net defined by OOA [i] based on OOA(229, 8199, S2, 5, 5), using
- digital (129, 140, 4194301)-net over F2, using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OOA(2140, large, F2, 3, 11), using
- net defined by OOA [i] based on linear OOA(2140, 4194301, F2, 15, 11) (dual of [(4194301, 15), 62914375, 12]-NRT-code), using
- (24, 29, 8199)-net in base 2, using
(169−11, 169, large)-Net over F2 — Digital
Digital (158, 169, large)-net over F2, using
- 217 times duplication [i] based on digital (141, 152, large)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, large, F2, 3, 11), using
- 4 times NRT-code embedding in larger space [i] based on linear OOA(2140, large, F2, 3, 11), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2152, large, F2, 3, 11), using
(169−11, 169, large)-Net in Base 2 — Upper bound on s
There is no (158, 169, large)-net in base 2, because
- 9 times m-reduction [i] would yield (158, 160, large)-net in base 2, but