Best Known (162, 173, s)-Nets in Base 2
(162, 173, 4227070)-Net over F2 — Constructive and digital
Digital (162, 173, 4227070)-net over F2, using
- 21 times duplication [i] based on digital (161, 172, 4227070)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (27, 32, 32769)-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
(162, 173, 4227077)-Net in Base 2 — Constructive
(162, 173, 4227077)-net in base 2, using
- (u, u+v)-construction [i] based on
- (28, 33, 32776)-net in base 2, using
- net defined by OOA [i] based on OOA(233, 32776, S2, 5, 5), using
- OOA 2-folding and stacking with additional row [i] based on OA(233, 65553, S2, 5), using
- construction X4 applied to RM(1,16) ⊂ K(16) [i] based on
- OA(232, 65536, S2, 5), using Kerdock OA K(16) [i]
- linear OA(217, 65536, F2, 3) (dual of [65536, 65519, 4]-code or 65536-cap in PG(16,2)), using Reed–Muller code RM(1,16) [i]
- linear OA(216, 17, F2, 15) (dual of [17, 1, 16]-code), using
- strength reduction [i] based on linear OA(216, 17, F2, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
- dual of repetition code with length 17 [i]
- strength reduction [i] based on linear OA(216, 17, F2, 16) (dual of [17, 1, 17]-code or 17-arc in PG(15,2)), using
- linear OA(21, 17, F2, 1) (dual of [17, 16, 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(1,16) ⊂ K(16) [i] based on
- OOA 2-folding and stacking with additional row [i] based on OA(233, 65553, S2, 5), using
- net defined by OOA [i] based on OOA(233, 32776, 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
- (28, 33, 32776)-net in base 2, using
(162, 173, large)-Net over F2 — Digital
Digital (162, 173, large)-net over F2, using
- 221 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
(162, 173, large)-Net in Base 2 — Upper bound on s
There is no (162, 173, large)-net in base 2, because
- 9 times m-reduction [i] would yield (162, 164, large)-net in base 2, but