Best Known (100, 100+28, s)-Nets in Base 16
(100, 100+28, 9407)-Net over F16 — Constructive and digital
Digital (100, 128, 9407)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (4, 18, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-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 (4, 18, 45)-net over F16, using
(100, 100+28, 18725)-Net in Base 16 — Constructive
(100, 128, 18725)-net in base 16, using
- 1 times m-reduction [i] based on (100, 129, 18725)-net in base 16, using
- base change [i] based on digital (57, 86, 18725)-net over F64, using
- net defined by OOA [i] based on linear OOA(6486, 18725, F64, 29, 29) (dual of [(18725, 29), 542939, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(6486, 262151, F64, 29) (dual of [262151, 262065, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(6486, 262152, F64, 29) (dual of [262152, 262066, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- linear OA(6485, 262145, F64, 29) (dual of [262145, 262060, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(6479, 262145, F64, 27) (dual of [262145, 262066, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 262145 | 646−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(641, 7, F64, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(641, s, F64, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- discarding factors / shortening the dual code based on linear OA(6486, 262152, F64, 29) (dual of [262152, 262066, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(6486, 262151, F64, 29) (dual of [262151, 262065, 30]-code), using
- net defined by OOA [i] based on linear OOA(6486, 18725, F64, 29, 29) (dual of [(18725, 29), 542939, 30]-NRT-code), using
- base change [i] based on digital (57, 86, 18725)-net over F64, using
(100, 100+28, 372179)-Net over F16 — Digital
Digital (100, 128, 372179)-net over F16, using
(100, 100+28, large)-Net in Base 16 — Upper bound on s
There is no (100, 128, large)-net in base 16, because
- 26 times m-reduction [i] would yield (100, 102, large)-net in base 16, but