Best Known (199−30, 199, s)-Nets in Base 4
(199−30, 199, 17476)-Net over F4 — Constructive and digital
Digital (169, 199, 17476)-net over F4, using
- net defined by OOA [i] based on linear OOA(4199, 17476, F4, 30, 30) (dual of [(17476, 30), 524081, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(4199, 262140, F4, 30) (dual of [262140, 261941, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4199, 262144, F4, 30) (dual of [262144, 261945, 31]-code), using
- an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- discarding factors / shortening the dual code based on linear OA(4199, 262144, F4, 30) (dual of [262144, 261945, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(4199, 262140, F4, 30) (dual of [262140, 261941, 31]-code), using
(199−30, 199, 89948)-Net over F4 — Digital
Digital (169, 199, 89948)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4199, 89948, F4, 2, 30) (dual of [(89948, 2), 179697, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4199, 131076, F4, 2, 30) (dual of [(131076, 2), 261953, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4199, 262152, F4, 30) (dual of [262152, 261953, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4199, 262153, F4, 30) (dual of [262153, 261954, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(4199, 262144, F4, 30) (dual of [262144, 261945, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(40, 9, F4, 0) (dual of [9, 9, 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(29) ⊂ Ce(28) [i] based on
- discarding factors / shortening the dual code based on linear OA(4199, 262153, F4, 30) (dual of [262153, 261954, 31]-code), using
- OOA 2-folding [i] based on linear OA(4199, 262152, F4, 30) (dual of [262152, 261953, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(4199, 131076, F4, 2, 30) (dual of [(131076, 2), 261953, 31]-NRT-code), using
(199−30, 199, large)-Net in Base 4 — Upper bound on s
There is no (169, 199, large)-net in base 4, because
- 28 times m-reduction [i] would yield (169, 171, large)-net in base 4, but