Best Known (205, 221, s)-Nets in Base 2
(205, 221, 1048705)-Net over F2 — Constructive and digital
Digital (205, 221, 1048705)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (29, 37, 130)-net over F2, using
- net defined by OOA [i] based on linear OOA(237, 130, F2, 8, 8) (dual of [(130, 8), 1003, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(237, 520, F2, 8) (dual of [520, 483, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(237, 522, F2, 8) (dual of [522, 485, 9]-code), using
- 1 times truncation [i] based on linear OA(238, 523, F2, 9) (dual of [523, 485, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(237, 512, F2, 9) (dual of [512, 475, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(228, 512, F2, 7) (dual of [512, 484, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(210, 11, F2, 9) (dual of [11, 1, 10]-code), using
- strength reduction [i] based on linear OA(210, 11, F2, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,2)), using
- dual of repetition code with length 11 [i]
- strength reduction [i] based on linear OA(210, 11, F2, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,2)), using
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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(8) ⊂ Ce(6) [i] based on
- 1 times truncation [i] based on linear OA(238, 523, F2, 9) (dual of [523, 485, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(237, 522, F2, 8) (dual of [522, 485, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(237, 520, F2, 8) (dual of [520, 483, 9]-code), using
- net defined by OOA [i] based on linear OOA(237, 130, F2, 8, 8) (dual of [(130, 8), 1003, 9]-NRT-code), using
- digital (168, 184, 1048575)-net over F2, using
- net defined by OOA [i] based on linear OOA(2184, 1048575, F2, 16, 16) (dual of [(1048575, 16), 16777016, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- net defined by OOA [i] based on linear OOA(2184, 1048575, F2, 16, 16) (dual of [(1048575, 16), 16777016, 17]-NRT-code), using
- digital (29, 37, 130)-net over F2, using
(205, 221, 2097411)-Net over F2 — Digital
Digital (205, 221, 2097411)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2221, 2097411, F2, 4, 16) (dual of [(2097411, 4), 8389423, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(237, 261, F2, 4, 8) (dual of [(261, 4), 1007, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(237, 261, F2, 2, 8) (dual of [(261, 2), 485, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(237, 522, F2, 8) (dual of [522, 485, 9]-code), using
- 1 times truncation [i] based on linear OA(238, 523, F2, 9) (dual of [523, 485, 10]-code), using
- construction X4 applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(237, 512, F2, 9) (dual of [512, 475, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(228, 512, F2, 7) (dual of [512, 484, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(210, 11, F2, 9) (dual of [11, 1, 10]-code), using
- strength reduction [i] based on linear OA(210, 11, F2, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,2)), using
- dual of repetition code with length 11 [i]
- strength reduction [i] based on linear OA(210, 11, F2, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,2)), using
- linear OA(21, 11, F2, 1) (dual of [11, 10, 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(8) ⊂ Ce(6) [i] based on
- 1 times truncation [i] based on linear OA(238, 523, F2, 9) (dual of [523, 485, 10]-code), using
- OOA 2-folding [i] based on linear OA(237, 522, F2, 8) (dual of [522, 485, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(237, 261, F2, 2, 8) (dual of [(261, 2), 485, 9]-NRT-code), using
- linear OOA(2184, 2097150, F2, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- linear OOA(237, 261, F2, 4, 8) (dual of [(261, 4), 1007, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(205, 221, large)-Net in Base 2 — Upper bound on s
There is no (205, 221, large)-net in base 2, because
- 14 times m-reduction [i] would yield (205, 207, large)-net in base 2, but