Best Known (153, 169, s)-Nets in Base 2
(153, 169, 262146)-Net over F2 — Constructive and digital
Digital (153, 169, 262146)-net over F2, using
- net defined by OOA [i] based on linear OOA(2169, 262146, F2, 16, 16) (dual of [(262146, 16), 4194167, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2169, 2097168, F2, 16) (dual of [2097168, 2096999, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2169, 2097174, F2, 16) (dual of [2097174, 2097005, 17]-code), using
- 1 times truncation [i] based on linear OA(2170, 2097175, F2, 17) (dual of [2097175, 2097005, 18]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2169, 2097152, F2, 17) (dual of [2097152, 2096983, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2148, 2097152, F2, 15) (dual of [2097152, 2097004, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(222, 23, F2, 21) (dual of [23, 1, 22]-code), using
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- dual of repetition code with length 23 [i]
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- linear OA(21, 23, F2, 1) (dual of [23, 22, 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 Ce(16) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(2170, 2097175, F2, 17) (dual of [2097175, 2097005, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2169, 2097174, F2, 16) (dual of [2097174, 2097005, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2169, 2097168, F2, 16) (dual of [2097168, 2096999, 17]-code), using
(153, 169, 391609)-Net over F2 — Digital
Digital (153, 169, 391609)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2169, 391609, F2, 5, 16) (dual of [(391609, 5), 1957876, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2169, 419434, F2, 5, 16) (dual of [(419434, 5), 2097001, 17]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2169, 2097170, F2, 16) (dual of [2097170, 2097001, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2169, 2097174, F2, 16) (dual of [2097174, 2097005, 17]-code), using
- 1 times truncation [i] based on linear OA(2170, 2097175, F2, 17) (dual of [2097175, 2097005, 18]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(14) [i] based on
- linear OA(2169, 2097152, F2, 17) (dual of [2097152, 2096983, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(2148, 2097152, F2, 15) (dual of [2097152, 2097004, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 221−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(222, 23, F2, 21) (dual of [23, 1, 22]-code), using
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- dual of repetition code with length 23 [i]
- strength reduction [i] based on linear OA(222, 23, F2, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,2)), using
- linear OA(21, 23, F2, 1) (dual of [23, 22, 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 Ce(16) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(2170, 2097175, F2, 17) (dual of [2097175, 2097005, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2169, 2097174, F2, 16) (dual of [2097174, 2097005, 17]-code), using
- OOA 5-folding [i] based on linear OA(2169, 2097170, F2, 16) (dual of [2097170, 2097001, 17]-code), using
- discarding factors / shortening the dual code based on linear OOA(2169, 419434, F2, 5, 16) (dual of [(419434, 5), 2097001, 17]-NRT-code), using
(153, 169, large)-Net in Base 2 — Upper bound on s
There is no (153, 169, large)-net in base 2, because
- 14 times m-reduction [i] would yield (153, 155, large)-net in base 2, but