Best Known (218−35, 218, s)-Nets in Base 4
(218−35, 218, 3857)-Net over F4 — Constructive and digital
Digital (183, 218, 3857)-net over F4, using
- 42 times duplication [i] based on digital (181, 216, 3857)-net over F4, using
- net defined by OOA [i] based on linear OOA(4216, 3857, F4, 35, 35) (dual of [(3857, 35), 134779, 36]-NRT-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(4216, 65570, F4, 35) (dual of [65570, 65354, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(4216, 65575, F4, 35) (dual of [65575, 65359, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(29) [i] based on
- linear OA(4209, 65536, F4, 35) (dual of [65536, 65327, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(34) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(4216, 65575, F4, 35) (dual of [65575, 65359, 36]-code), using
- OOA 17-folding and stacking with additional row [i] based on linear OA(4216, 65570, F4, 35) (dual of [65570, 65354, 36]-code), using
- net defined by OOA [i] based on linear OOA(4216, 3857, F4, 35, 35) (dual of [(3857, 35), 134779, 36]-NRT-code), using
(218−35, 218, 39897)-Net over F4 — Digital
Digital (183, 218, 39897)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4218, 39897, F4, 35) (dual of [39897, 39679, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(4218, 65577, F4, 35) (dual of [65577, 65359, 36]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4216, 65575, F4, 35) (dual of [65575, 65359, 36]-code), using
- construction X applied to Ce(34) ⊂ Ce(29) [i] based on
- linear OA(4209, 65536, F4, 35) (dual of [65536, 65327, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(47, 39, F4, 4) (dual of [39, 32, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(34) ⊂ Ce(29) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(4216, 65575, F4, 35) (dual of [65575, 65359, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(4218, 65577, F4, 35) (dual of [65577, 65359, 36]-code), using
(218−35, 218, large)-Net in Base 4 — Upper bound on s
There is no (183, 218, large)-net in base 4, because
- 33 times m-reduction [i] would yield (183, 185, large)-net in base 4, but