Best Known (22, 36, s)-Nets in Base 128
(22, 36, 2491)-Net over F128 — Constructive and digital
Digital (22, 36, 2491)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (14, 28, 2341)-net over F128, using
- net defined by OOA [i] based on linear OOA(12828, 2341, F128, 14, 14) (dual of [(2341, 14), 32746, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(12828, 16387, F128, 14) (dual of [16387, 16359, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(12828, 16389, F128, 14) (dual of [16389, 16361, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- linear OA(12827, 16384, F128, 14) (dual of [16384, 16357, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(12823, 16384, F128, 12) (dual of [16384, 16361, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(1281, 5, F128, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(1281, s, F128, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(12828, 16389, F128, 14) (dual of [16389, 16361, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(12828, 16387, F128, 14) (dual of [16387, 16359, 15]-code), using
- net defined by OOA [i] based on linear OOA(12828, 2341, F128, 14, 14) (dual of [(2341, 14), 32746, 15]-NRT-code), using
- digital (1, 8, 150)-net over F128, using
(22, 36, 9364)-Net in Base 128 — Constructive
(22, 36, 9364)-net in base 128, using
- net defined by OOA [i] based on OOA(12836, 9364, S128, 14, 14), using
- OA 7-folding and stacking [i] based on OA(12836, 65548, S128, 14), using
- discarding factors based on OA(12836, 65550, S128, 14), using
- discarding parts of the base [i] based on linear OA(25631, 65550, F256, 14) (dual of [65550, 65519, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- linear OA(25627, 65536, F256, 14) (dual of [65536, 65509, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(25617, 65536, F256, 9) (dual of [65536, 65519, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(2564, 14, F256, 4) (dual of [14, 10, 5]-code or 14-arc in PG(3,256)), using
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- Reed–Solomon code RS(252,256) [i]
- discarding factors / shortening the dual code based on linear OA(2564, 256, F256, 4) (dual of [256, 252, 5]-code or 256-arc in PG(3,256)), using
- construction X applied to Ce(13) ⊂ Ce(8) [i] based on
- discarding parts of the base [i] based on linear OA(25631, 65550, F256, 14) (dual of [65550, 65519, 15]-code), using
- discarding factors based on OA(12836, 65550, S128, 14), using
- OA 7-folding and stacking [i] based on OA(12836, 65548, S128, 14), using
(22, 36, 30552)-Net over F128 — Digital
Digital (22, 36, 30552)-net over F128, using
(22, 36, large)-Net in Base 128 — Upper bound on s
There is no (22, 36, large)-net in base 128, because
- 12 times m-reduction [i] would yield (22, 24, large)-net in base 128, but