Best Known (22, 22+5, s)-Nets in Base 4
(22, 22+5, 65281)-Net over F4 — Constructive and digital
Digital (22, 27, 65281)-net over F4, using
- net defined by OOA [i] based on linear OOA(427, 65281, F4, 5, 5) (dual of [(65281, 5), 326378, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(427, 130563, F4, 5) (dual of [130563, 130536, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(426, 130562, F4, 5) (dual of [130562, 130536, 6]-code), using
- trace code [i] based on linear OA(1613, 65281, F16, 5) (dual of [65281, 65268, 6]-code), using
- 1 times code embedding in larger space [i] based on linear OA(426, 130562, F4, 5) (dual of [130562, 130536, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(427, 130563, F4, 5) (dual of [130563, 130536, 6]-code), using
(22, 22+5, 100025)-Net over F4 — Digital
Digital (22, 27, 100025)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(427, 100025, F4, 5) (dual of [100025, 99998, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(427, 130562, F4, 5) (dual of [130562, 130535, 6]-code), using
- base reduction for projective spaces (embedding PG(13,16) in PG(26,4)) [i] based on linear OA(1614, 130562, F16, 5) (dual of [130562, 130548, 6]-code), using
- trace code [i] based on linear OA(2567, 65281, F256, 5) (dual of [65281, 65274, 6]-code), using
- base reduction for projective spaces (embedding PG(13,16) in PG(26,4)) [i] based on linear OA(1614, 130562, F16, 5) (dual of [130562, 130548, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(427, 130562, F4, 5) (dual of [130562, 130535, 6]-code), using
(22, 22+5, large)-Net in Base 4 — Upper bound on s
There is no (22, 27, large)-net in base 4, because
- 3 times m-reduction [i] would yield (22, 24, large)-net in base 4, but