Best Known (76, 76+14, s)-Nets in Base 2
(76, 76+14, 589)-Net over F2 — Constructive and digital
Digital (76, 90, 589)-net over F2, using
- net defined by OOA [i] based on linear OOA(290, 589, F2, 14, 14) (dual of [(589, 14), 8156, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(290, 4123, F2, 14) (dual of [4123, 4033, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(290, 4125, F2, 14) (dual of [4125, 4035, 15]-code), using
- 1 times truncation [i] based on linear OA(291, 4126, F2, 15) (dual of [4126, 4035, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(285, 4096, F2, 15) (dual of [4096, 4011, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(261, 4096, F2, 11) (dual of [4096, 4035, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(291, 4126, F2, 15) (dual of [4126, 4035, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(290, 4125, F2, 14) (dual of [4125, 4035, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(290, 4123, F2, 14) (dual of [4123, 4033, 15]-code), using
(76, 76+14, 1375)-Net over F2 — Digital
Digital (76, 90, 1375)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(290, 1375, F2, 3, 14) (dual of [(1375, 3), 4035, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(290, 4125, F2, 14) (dual of [4125, 4035, 15]-code), using
- 1 times truncation [i] based on linear OA(291, 4126, F2, 15) (dual of [4126, 4035, 16]-code), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- linear OA(285, 4096, F2, 15) (dual of [4096, 4011, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(261, 4096, F2, 11) (dual of [4096, 4035, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 4095 = 212−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(26, 30, F2, 3) (dual of [30, 24, 4]-code or 30-cap in PG(5,2)), using
- discarding factors / shortening the dual code based on linear OA(26, 32, F2, 3) (dual of [32, 26, 4]-code or 32-cap in PG(5,2)), using
- construction X applied to Ce(14) ⊂ Ce(10) [i] based on
- 1 times truncation [i] based on linear OA(291, 4126, F2, 15) (dual of [4126, 4035, 16]-code), using
- OOA 3-folding [i] based on linear OA(290, 4125, F2, 14) (dual of [4125, 4035, 15]-code), using
(76, 76+14, 25068)-Net in Base 2 — Upper bound on s
There is no (76, 90, 25069)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 1238 057339 336604 858430 041640 > 290 [i]