Best Known (114−20, 114, s)-Nets in Base 4
(114−20, 114, 1642)-Net over F4 — Constructive and digital
Digital (94, 114, 1642)-net over F4, using
- net defined by OOA [i] based on linear OOA(4114, 1642, F4, 20, 20) (dual of [(1642, 20), 32726, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(4114, 16420, F4, 20) (dual of [16420, 16306, 21]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4113, 16419, F4, 20) (dual of [16419, 16306, 21]-code), using
- construction X applied to Ce(20) ⊂ 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(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(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(20) ⊂ Ce(14) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4113, 16419, F4, 20) (dual of [16419, 16306, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(4114, 16420, F4, 20) (dual of [16420, 16306, 21]-code), using
(114−20, 114, 15143)-Net over F4 — Digital
Digital (94, 114, 15143)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4114, 15143, F4, 20) (dual of [15143, 15029, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(4114, 16407, F4, 20) (dual of [16407, 16293, 21]-code), using
- construction X4 applied to Ce(21) ⊂ Ce(17) [i] based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(422, 23, F4, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,4)), using
- dual of repetition code with length 23 [i]
- linear OA(41, 23, F4, 1) (dual of [23, 22, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X4 applied to Ce(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4114, 16407, F4, 20) (dual of [16407, 16293, 21]-code), using
(114−20, 114, large)-Net in Base 4 — Upper bound on s
There is no (94, 114, large)-net in base 4, because
- 18 times m-reduction [i] would yield (94, 96, large)-net in base 4, but