Best Known (98, 117, s)-Nets in Base 4
(98, 117, 7284)-Net over F4 — Constructive and digital
Digital (98, 117, 7284)-net over F4, using
- net defined by OOA [i] based on linear OOA(4117, 7284, F4, 19, 19) (dual of [(7284, 19), 138279, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4117, 65557, F4, 19) (dual of [65557, 65440, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4117, 65558, F4, 19) (dual of [65558, 65441, 20]-code), using
- construction XX applied to Ce(18) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- linear OA(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(41, 19, F4, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- construction XX applied to Ce(18) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- discarding factors / shortening the dual code based on linear OA(4117, 65558, F4, 19) (dual of [65558, 65441, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4117, 65557, F4, 19) (dual of [65557, 65440, 20]-code), using
(98, 117, 32779)-Net over F4 — Digital
Digital (98, 117, 32779)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4117, 32779, F4, 2, 19) (dual of [(32779, 2), 65441, 20]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4117, 65558, F4, 19) (dual of [65558, 65441, 20]-code), using
- construction XX applied to Ce(18) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- linear OA(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 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(489, 65536, F4, 15) (dual of [65536, 65447, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(41, 19, F4, 1) (dual of [19, 18, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- linear OA(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- construction XX applied to Ce(18) ⊂ Ce(16) ⊂ Ce(14) [i] based on
- OOA 2-folding [i] based on linear OA(4117, 65558, F4, 19) (dual of [65558, 65441, 20]-code), using
(98, 117, large)-Net in Base 4 — Upper bound on s
There is no (98, 117, large)-net in base 4, because
- 17 times m-reduction [i] would yield (98, 100, large)-net in base 4, but