Best Known (171, 171+30, s)-Nets in Base 4
(171, 171+30, 17477)-Net over F4 — Constructive and digital
Digital (171, 201, 17477)-net over F4, using
- net defined by OOA [i] based on linear OOA(4201, 17477, F4, 30, 30) (dual of [(17477, 30), 524109, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(4201, 262155, F4, 30) (dual of [262155, 261954, 31]-code), using
- 2 times code embedding in larger space [i] 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
- 2 times code embedding in larger space [i] based on linear OA(4199, 262153, F4, 30) (dual of [262153, 261954, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(4201, 262155, F4, 30) (dual of [262155, 261954, 31]-code), using
(171, 171+30, 99677)-Net over F4 — Digital
Digital (171, 201, 99677)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4201, 99677, F4, 2, 30) (dual of [(99677, 2), 199153, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4201, 131077, F4, 2, 30) (dual of [(131077, 2), 261953, 31]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4200, 131077, F4, 2, 30) (dual of [(131077, 2), 261954, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4200, 262154, F4, 30) (dual of [262154, 261954, 31]-code), using
- 1 times code embedding in larger space [i] 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
- 1 times code embedding in larger space [i] based on linear OA(4199, 262153, F4, 30) (dual of [262153, 261954, 31]-code), using
- OOA 2-folding [i] based on linear OA(4200, 262154, F4, 30) (dual of [262154, 261954, 31]-code), using
- 41 times duplication [i] based on linear OOA(4200, 131077, F4, 2, 30) (dual of [(131077, 2), 261954, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4201, 131077, F4, 2, 30) (dual of [(131077, 2), 261953, 31]-NRT-code), using
(171, 171+30, large)-Net in Base 4 — Upper bound on s
There is no (171, 201, large)-net in base 4, because
- 28 times m-reduction [i] would yield (171, 173, large)-net in base 4, but