Best Known (118, 118+16, s)-Nets in Base 4
(118, 118+16, 524291)-Net over F4 — Constructive and digital
Digital (118, 134, 524291)-net over F4, using
- net defined by OOA [i] based on linear OOA(4134, 524291, F4, 16, 16) (dual of [(524291, 16), 8388522, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4134, 4194328, F4, 16) (dual of [4194328, 4194194, 17]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 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
- construction X4 applied to Ce(16) ⊂ Ce(13) [i] based on
- OA 8-folding and stacking [i] based on linear OA(4134, 4194328, F4, 16) (dual of [4194328, 4194194, 17]-code), using
(118, 118+16, 2097164)-Net over F4 — Digital
Digital (118, 134, 2097164)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4134, 2097164, F4, 2, 16) (dual of [(2097164, 2), 4194194, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4134, 4194328, F4, 16) (dual of [4194328, 4194194, 17]-code), using
- construction X4 applied to Ce(16) ⊂ Ce(13) [i] based on
- linear OA(4133, 4194304, F4, 17) (dual of [4194304, 4194171, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(4111, 4194304, F4, 14) (dual of [4194304, 4194193, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(423, 24, F4, 23) (dual of [24, 1, 24]-code or 24-arc in PG(22,4)), using
- dual of repetition code with length 24 [i]
- linear OA(41, 24, F4, 1) (dual of [24, 23, 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
- construction X4 applied to Ce(16) ⊂ Ce(13) [i] based on
- OOA 2-folding [i] based on linear OA(4134, 4194328, F4, 16) (dual of [4194328, 4194194, 17]-code), using
(118, 118+16, large)-Net in Base 4 — Upper bound on s
There is no (118, 134, large)-net in base 4, because
- 14 times m-reduction [i] would yield (118, 120, large)-net in base 4, but