Best Known (183−29, 183, s)-Nets in Base 4
(183−29, 183, 4686)-Net over F4 — Constructive and digital
Digital (154, 183, 4686)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 14, 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 (140, 169, 4681)-net over F4, using
- net defined by OOA [i] based on linear OOA(4169, 4681, F4, 29, 29) (dual of [(4681, 29), 135580, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4169, 65535, F4, 29) (dual of [65535, 65366, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4169, 65535, F4, 29) (dual of [65535, 65366, 30]-code), using
- net defined by OOA [i] based on linear OOA(4169, 4681, F4, 29, 29) (dual of [(4681, 29), 135580, 30]-NRT-code), using
- digital (0, 14, 5)-net over F4, using
(183−29, 183, 41629)-Net over F4 — Digital
Digital (154, 183, 41629)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4183, 41629, F4, 29) (dual of [41629, 41446, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4183, 65551, F4, 29) (dual of [65551, 65368, 30]-code), using
- (u, u+v)-construction [i] based on
- linear OA(414, 15, F4, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,4)), using
- dual of repetition code with length 15 [i]
- linear OA(4169, 65536, F4, 29) (dual of [65536, 65367, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(414, 15, F4, 14) (dual of [15, 1, 15]-code or 15-arc in PG(13,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4183, 65551, F4, 29) (dual of [65551, 65368, 30]-code), using
(183−29, 183, large)-Net in Base 4 — Upper bound on s
There is no (154, 183, large)-net in base 4, because
- 27 times m-reduction [i] would yield (154, 156, large)-net in base 4, but