Best Known (193, 193+23, s)-Nets in Base 4
(193, 193+23, 762605)-Net over F4 — Constructive and digital
Digital (193, 216, 762605)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 5)-net over F4, using
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 0 and N(F) ≥ 5, using
- the rational function field F4(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 4)-sequence over F4, using
- digital (182, 205, 762600)-net over F4, using
- net defined by OOA [i] based on linear OOA(4205, 762600, F4, 23, 23) (dual of [(762600, 23), 17539595, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4205, 8388601, F4, 23) (dual of [8388601, 8388396, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4205, large, F4, 23) (dual of [large, large−205, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(4205, large, F4, 23) (dual of [large, large−205, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4205, 8388601, F4, 23) (dual of [8388601, 8388396, 24]-code), using
- net defined by OOA [i] based on linear OOA(4205, 762600, F4, 23, 23) (dual of [(762600, 23), 17539595, 24]-NRT-code), using
- digital (0, 11, 5)-net over F4, using
(193, 193+23, 4220046)-Net over F4 — Digital
Digital (193, 216, 4220046)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4216, 4220046, F4, 23) (dual of [4220046, 4219830, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4216, large, F4, 23) (dual of [large, large−216, 24]-code), using
- strength reduction [i] based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- strength reduction [i] based on linear OA(4216, large, F4, 24) (dual of [large, large−216, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4216, large, F4, 23) (dual of [large, large−216, 24]-code), using
(193, 193+23, large)-Net in Base 4 — Upper bound on s
There is no (193, 216, large)-net in base 4, because
- 21 times m-reduction [i] would yield (193, 195, large)-net in base 4, but