Best Known (178, 207, s)-Nets in Base 4
(178, 207, 18738)-Net over F4 — Constructive and digital
Digital (178, 207, 18738)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (3, 17, 14)-net over F4, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 3 and N(F) ≥ 14, using
- net from sequence [i] based on digital (3, 13)-sequence over F4, using
- digital (161, 190, 18724)-net over F4, using
- net defined by OOA [i] based on linear OOA(4190, 18724, F4, 29, 29) (dual of [(18724, 29), 542806, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4190, 262137, F4, 29) (dual of [262137, 261947, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(4190, 262137, F4, 29) (dual of [262137, 261947, 30]-code), using
- net defined by OOA [i] based on linear OOA(4190, 18724, F4, 29, 29) (dual of [(18724, 29), 542806, 30]-NRT-code), using
- digital (3, 17, 14)-net over F4, using
(178, 207, 142796)-Net over F4 — Digital
Digital (178, 207, 142796)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4207, 142796, F4, 29) (dual of [142796, 142589, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(4207, 262164, F4, 29) (dual of [262164, 261957, 30]-code), using
- (u, u+v)-construction [i] based on
- linear OA(417, 20, F4, 14) (dual of [20, 3, 15]-code), using
- 1 times truncation [i] based on linear OA(418, 21, F4, 15) (dual of [21, 3, 16]-code), using
- Simplex code S(3,4) [i]
- 1 times truncation [i] based on linear OA(418, 21, F4, 15) (dual of [21, 3, 16]-code), using
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(417, 20, F4, 14) (dual of [20, 3, 15]-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4207, 262164, F4, 29) (dual of [262164, 261957, 30]-code), using
(178, 207, large)-Net in Base 4 — Upper bound on s
There is no (178, 207, large)-net in base 4, because
- 27 times m-reduction [i] would yield (178, 180, large)-net in base 4, but