Best Known (85, 85+16, s)-Nets in Base 4
(85, 85+16, 8195)-Net over F4 — Constructive and digital
Digital (85, 101, 8195)-net over F4, using
- net defined by OOA [i] based on linear OOA(4101, 8195, F4, 16, 16) (dual of [(8195, 16), 131019, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4101, 65560, F4, 16) (dual of [65560, 65459, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4101, 65564, F4, 16) (dual of [65564, 65463, 17]-code), using
- 1 times truncation [i] based on linear OA(4102, 65565, F4, 17) (dual of [65565, 65463, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [i] based on
- 1 times truncation [i] based on linear OA(4102, 65565, F4, 17) (dual of [65565, 65463, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4101, 65564, F4, 16) (dual of [65564, 65463, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(4101, 65560, F4, 16) (dual of [65560, 65459, 17]-code), using
(85, 85+16, 40239)-Net over F4 — Digital
Digital (85, 101, 40239)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4101, 40239, F4, 16) (dual of [40239, 40138, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4101, 65564, F4, 16) (dual of [65564, 65463, 17]-code), using
- 1 times truncation [i] based on linear OA(4102, 65565, F4, 17) (dual of [65565, 65463, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(497, 65536, F4, 17) (dual of [65536, 65439, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(473, 65536, F4, 13) (dual of [65536, 65463, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [i] based on
- 1 times truncation [i] based on linear OA(4102, 65565, F4, 17) (dual of [65565, 65463, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4101, 65564, F4, 16) (dual of [65564, 65463, 17]-code), using
(85, 85+16, large)-Net in Base 4 — Upper bound on s
There is no (85, 101, large)-net in base 4, because
- 14 times m-reduction [i] would yield (85, 87, large)-net in base 4, but