Best Known (180−16, 180, s)-Nets in Base 4
(180−16, 180, 2097150)-Net over F4 — Constructive and digital
Digital (164, 180, 2097150)-net over F4, using
- net defined by OOA [i] based on linear OOA(4180, 2097150, F4, 18, 16) (dual of [(2097150, 18), 37748520, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4180, 8388601, F4, 2, 16) (dual of [(8388601, 2), 16777022, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4180, 8388602, F4, 2, 16) (dual of [(8388602, 2), 16777024, 17]-NRT-code), using
- trace code [i] based on linear OOA(1690, 4194301, F16, 2, 16) (dual of [(4194301, 2), 8388512, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(1690, 8388602, F16, 16) (dual of [8388602, 8388512, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(1690, large, F16, 16) (dual of [large, large−90, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 166−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(1690, large, F16, 16) (dual of [large, large−90, 17]-code), using
- OOA 2-folding [i] based on linear OA(1690, 8388602, F16, 16) (dual of [8388602, 8388512, 17]-code), using
- trace code [i] based on linear OOA(1690, 4194301, F16, 2, 16) (dual of [(4194301, 2), 8388512, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4180, 8388602, F4, 2, 16) (dual of [(8388602, 2), 16777024, 17]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OOA(4180, 8388601, F4, 2, 16) (dual of [(8388601, 2), 16777022, 17]-NRT-code), using
(180−16, 180, large)-Net over F4 — Digital
Digital (164, 180, large)-net over F4, using
- 44 times duplication [i] based on digital (160, 176, large)-net over F4, using
- t-expansion [i] based on digital (158, 176, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4176, large, F4, 18) (dual of [large, large−176, 19]-code), using
- 19 times code embedding in larger space [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- 19 times code embedding in larger space [i] based on linear OA(4157, large, F4, 18) (dual of [large, large−157, 19]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4176, large, F4, 18) (dual of [large, large−176, 19]-code), using
- t-expansion [i] based on digital (158, 176, large)-net over F4, using
(180−16, 180, large)-Net in Base 4 — Upper bound on s
There is no (164, 180, large)-net in base 4, because
- 14 times m-reduction [i] would yield (164, 166, large)-net in base 4, but