Best Known (94, 94+21, s)-Nets in Base 4
(94, 94+21, 1641)-Net over F4 — Constructive and digital
Digital (94, 115, 1641)-net over F4, using
- 43 times duplication [i] based on digital (91, 112, 1641)-net over F4, using
- net defined by OOA [i] based on linear OOA(4112, 1641, F4, 21, 21) (dual of [(1641, 21), 34349, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4112, 16411, F4, 21) (dual of [16411, 16299, 22]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4111, 16410, F4, 21) (dual of [16410, 16299, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(45, 26, F4, 3) (dual of [26, 21, 4]-code or 26-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(20) ⊂ Ce(16) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4111, 16410, F4, 21) (dual of [16410, 16299, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4112, 16411, F4, 21) (dual of [16411, 16299, 22]-code), using
- net defined by OOA [i] based on linear OOA(4112, 1641, F4, 21, 21) (dual of [(1641, 21), 34349, 22]-NRT-code), using
(94, 94+21, 10811)-Net over F4 — Digital
Digital (94, 115, 10811)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4115, 10811, F4, 21) (dual of [10811, 10696, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4115, 16417, F4, 21) (dual of [16417, 16302, 22]-code), using
- construction XX applied to Ce(20) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(478, 16384, F4, 15) (dual of [16384, 16306, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(45, 29, F4, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- construction XX applied to Ce(20) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4115, 16417, F4, 21) (dual of [16417, 16302, 22]-code), using
(94, 94+21, large)-Net in Base 4 — Upper bound on s
There is no (94, 115, large)-net in base 4, because
- 19 times m-reduction [i] would yield (94, 96, large)-net in base 4, but