Best Known (96, 96+28, s)-Nets in Base 16
(96, 96+28, 9379)-Net over F16 — Constructive and digital
Digital (96, 124, 9379)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 14, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (82, 110, 9362)-net over F16, using
- net defined by OOA [i] based on linear OOA(16110, 9362, F16, 28, 28) (dual of [(9362, 28), 262026, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(16110, 131068, F16, 28) (dual of [131068, 130958, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16110, 131072, F16, 28) (dual of [131072, 130962, 29]-code), using
- trace code [i] based on linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- trace code [i] based on linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16110, 131072, F16, 28) (dual of [131072, 130962, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(16110, 131068, F16, 28) (dual of [131068, 130958, 29]-code), using
- net defined by OOA [i] based on linear OOA(16110, 9362, F16, 28, 28) (dual of [(9362, 28), 262026, 29]-NRT-code), using
- digital (0, 14, 17)-net over F16, using
(96, 96+28, 18724)-Net in Base 16 — Constructive
(96, 124, 18724)-net in base 16, using
- 161 times duplication [i] based on (95, 123, 18724)-net in base 16, using
- base change [i] based on digital (54, 82, 18724)-net over F64, using
- net defined by OOA [i] based on linear OOA(6482, 18724, F64, 28, 28) (dual of [(18724, 28), 524190, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(6482, 262136, F64, 28) (dual of [262136, 262054, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(6482, 262144, F64, 28) (dual of [262144, 262062, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(6482, 262136, F64, 28) (dual of [262136, 262054, 29]-code), using
- net defined by OOA [i] based on linear OOA(6482, 18724, F64, 28, 28) (dual of [(18724, 28), 524190, 29]-NRT-code), using
- base change [i] based on digital (54, 82, 18724)-net over F64, using
(96, 96+28, 246815)-Net over F16 — Digital
Digital (96, 124, 246815)-net over F16, using
(96, 96+28, large)-Net in Base 16 — Upper bound on s
There is no (96, 124, large)-net in base 16, because
- 26 times m-reduction [i] would yield (96, 98, large)-net in base 16, but