Best Known (154, 154+31, s)-Nets in Base 4
(154, 154+31, 4369)-Net over F4 — Constructive and digital
Digital (154, 185, 4369)-net over F4, using
- net defined by OOA [i] based on linear OOA(4185, 4369, F4, 31, 31) (dual of [(4369, 31), 135254, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- OOA 15-folding and stacking with additional row [i] based on linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using
(154, 154+31, 32395)-Net over F4 — Digital
Digital (154, 185, 32395)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4185, 32395, F4, 2, 31) (dual of [(32395, 2), 64605, 32]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4185, 32772, F4, 2, 31) (dual of [(32772, 2), 65359, 32]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4185, 65544, F4, 31) (dual of [65544, 65359, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- linear OA(4185, 65536, F4, 31) (dual of [65536, 65351, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(4177, 65536, F4, 30) (dual of [65536, 65359, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(40, 8, F4, 0) (dual of [8, 8, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- OOA 2-folding [i] based on linear OA(4185, 65544, F4, 31) (dual of [65544, 65359, 32]-code), using
- discarding factors / shortening the dual code based on linear OOA(4185, 32772, F4, 2, 31) (dual of [(32772, 2), 65359, 32]-NRT-code), using
(154, 154+31, large)-Net in Base 4 — Upper bound on s
There is no (154, 185, large)-net in base 4, because
- 29 times m-reduction [i] would yield (154, 156, large)-net in base 4, but