Best Known (95, 95+21, s)-Nets in Base 4
(95, 95+21, 1643)-Net over F4 — Constructive and digital
Digital (95, 116, 1643)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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 (85, 106, 1638)-net over F4, using
- net defined by OOA [i] based on linear OOA(4106, 1638, F4, 21, 21) (dual of [(1638, 21), 34292, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4106, 16381, F4, 21) (dual of [16381, 16275, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4106, 16381, F4, 21) (dual of [16381, 16275, 22]-code), using
- net defined by OOA [i] based on linear OOA(4106, 1638, F4, 21, 21) (dual of [(1638, 21), 34292, 22]-NRT-code), using
- digital (0, 10, 5)-net over F4, using
(95, 95+21, 11630)-Net over F4 — Digital
Digital (95, 116, 11630)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4116, 11630, F4, 21) (dual of [11630, 11514, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4116, 16395, F4, 21) (dual of [16395, 16279, 22]-code), using
- (u, u+v)-construction [i] based on
- linear OA(410, 11, F4, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,4)), using
- dual of repetition code with length 11 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(410, 11, F4, 10) (dual of [11, 1, 11]-code or 11-arc in PG(9,4)), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OA(4116, 16395, F4, 21) (dual of [16395, 16279, 22]-code), using
(95, 95+21, large)-Net in Base 4 — Upper bound on s
There is no (95, 116, large)-net in base 4, because
- 19 times m-reduction [i] would yield (95, 97, large)-net in base 4, but