Best Known (132, 132+26, s)-Nets in Base 4
(132, 132+26, 5043)-Net over F4 — Constructive and digital
Digital (132, 158, 5043)-net over F4, using
- net defined by OOA [i] based on linear OOA(4158, 5043, F4, 26, 26) (dual of [(5043, 26), 130960, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4158, 65559, F4, 26) (dual of [65559, 65401, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4158, 65565, F4, 26) (dual of [65565, 65407, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(4158, 65565, F4, 26) (dual of [65565, 65407, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(4158, 65559, F4, 26) (dual of [65559, 65401, 27]-code), using
(132, 132+26, 32782)-Net over F4 — Digital
Digital (132, 158, 32782)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4158, 32782, F4, 2, 26) (dual of [(32782, 2), 65406, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4158, 65564, F4, 26) (dual of [65564, 65406, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4158, 65565, F4, 26) (dual of [65565, 65407, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(4153, 65536, F4, 26) (dual of [65536, 65383, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4129, 65536, F4, 22) (dual of [65536, 65407, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(4158, 65565, F4, 26) (dual of [65565, 65407, 27]-code), using
- OOA 2-folding [i] based on linear OA(4158, 65564, F4, 26) (dual of [65564, 65406, 27]-code), using
(132, 132+26, large)-Net in Base 4 — Upper bound on s
There is no (132, 158, large)-net in base 4, because
- 24 times m-reduction [i] would yield (132, 134, large)-net in base 4, but