Best Known (148, 177, s)-Nets in Base 4
(148, 177, 4683)-Net over F4 — Constructive and digital
Digital (148, 177, 4683)-net over F4, using
- 43 times duplication [i] based on digital (145, 174, 4683)-net over F4, using
- net defined by OOA [i] based on linear OOA(4174, 4683, F4, 29, 29) (dual of [(4683, 29), 135633, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4174, 65563, F4, 29) (dual of [65563, 65389, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4174, 65565, F4, 29) (dual of [65565, 65391, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(24) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(28) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(4174, 65565, F4, 29) (dual of [65565, 65391, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4174, 65563, F4, 29) (dual of [65563, 65389, 30]-code), using
- net defined by OOA [i] based on linear OOA(4174, 4683, F4, 29, 29) (dual of [(4683, 29), 135633, 30]-NRT-code), using
(148, 177, 32785)-Net over F4 — Digital
Digital (148, 177, 32785)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4177, 32785, F4, 2, 29) (dual of [(32785, 2), 65393, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4177, 65570, F4, 29) (dual of [65570, 65393, 30]-code), using
- construction XX applied to Ce(28) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4137, 65536, F4, 23) (dual of [65536, 65399, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(45, 31, F4, 3) (dual of [31, 26, 4]-code or 31-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, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- construction XX applied to Ce(28) ⊂ Ce(24) ⊂ Ce(22) [i] based on
- OOA 2-folding [i] based on linear OA(4177, 65570, F4, 29) (dual of [65570, 65393, 30]-code), using
(148, 177, large)-Net in Base 4 — Upper bound on s
There is no (148, 177, large)-net in base 4, because
- 27 times m-reduction [i] would yield (148, 150, large)-net in base 4, but