Best Known (192, 192+31, s)-Nets in Base 4
(192, 192+31, 17481)-Net over F4 — Constructive and digital
Digital (192, 223, 17481)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 15, 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 (177, 208, 17476)-net over F4, using
- net defined by OOA [i] based on linear OOA(4208, 17476, F4, 31, 31) (dual of [(17476, 31), 541548, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(4208, 262141, F4, 31) (dual of [262141, 261933, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(4208, 262144, F4, 31) (dual of [262144, 261936, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- discarding factors / shortening the dual code based on linear OA(4208, 262144, F4, 31) (dual of [262144, 261936, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(4208, 262141, F4, 31) (dual of [262141, 261933, 32]-code), using
- net defined by OOA [i] based on linear OOA(4208, 17476, F4, 31, 31) (dual of [(17476, 31), 541548, 32]-NRT-code), using
- digital (0, 15, 5)-net over F4, using
(192, 192+31, 158056)-Net over F4 — Digital
Digital (192, 223, 158056)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4223, 158056, F4, 31) (dual of [158056, 157833, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(4223, 262160, F4, 31) (dual of [262160, 261937, 32]-code), using
- (u, u+v)-construction [i] based on
- linear OA(415, 16, F4, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
- dual of repetition code with length 16 [i]
- linear OA(4208, 262144, F4, 31) (dual of [262144, 261936, 32]-code), using
- an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(415, 16, F4, 15) (dual of [16, 1, 16]-code or 16-arc in PG(14,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4223, 262160, F4, 31) (dual of [262160, 261937, 32]-code), using
(192, 192+31, large)-Net in Base 4 — Upper bound on s
There is no (192, 223, large)-net in base 4, because
- 29 times m-reduction [i] would yield (192, 194, large)-net in base 4, but