Best Known (103, 126, s)-Nets in Base 16
(103, 126, 95391)-Net over F16 — Constructive and digital
Digital (103, 126, 95391)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (9, 20, 66)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 7, 120)-net over F16, using
- net defined by OOA [i] based on linear OOA(167, 120, F16, 5, 5) (dual of [(120, 5), 593, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(167, 241, F16, 5) (dual of [241, 234, 6]-code), using
- net defined by OOA [i] based on linear OOA(167, 120, F16, 5, 5) (dual of [(120, 5), 593, 6]-NRT-code), using
- digital (2, 13, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (2, 7, 120)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (83, 106, 95325)-net over F16, using
- net defined by OOA [i] based on linear OOA(16106, 95325, F16, 23, 23) (dual of [(95325, 23), 2192369, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- OOA 11-folding and stacking with additional row [i] based on linear OA(16106, 1048576, F16, 23) (dual of [1048576, 1048470, 24]-code), using
- net defined by OOA [i] based on linear OOA(16106, 95325, F16, 23, 23) (dual of [(95325, 23), 2192369, 24]-NRT-code), using
- digital (9, 20, 66)-net over F16, using
(103, 126, 190652)-Net in Base 16 — Constructive
(103, 126, 190652)-net in base 16, using
- base change [i] based on digital (49, 72, 190652)-net over F128, using
- net defined by OOA [i] based on linear OOA(12872, 190652, F128, 23, 23) (dual of [(190652, 23), 4384924, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12872, 2097173, F128, 23) (dual of [2097173, 2097101, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(12872, 2097176, F128, 23) (dual of [2097176, 2097104, 24]-code), using
- construction X applied to C([0,11]) ⊂ C([0,8]) [i] based on
- linear OA(12867, 2097153, F128, 23) (dual of [2097153, 2097086, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(12849, 2097153, F128, 17) (dual of [2097153, 2097104, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 2097153 | 1286−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- linear OA(1285, 23, F128, 5) (dual of [23, 18, 6]-code or 23-arc in PG(4,128)), using
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- Reed–Solomon code RS(123,128) [i]
- discarding factors / shortening the dual code based on linear OA(1285, 128, F128, 5) (dual of [128, 123, 6]-code or 128-arc in PG(4,128)), using
- construction X applied to C([0,11]) ⊂ C([0,8]) [i] based on
- discarding factors / shortening the dual code based on linear OA(12872, 2097176, F128, 23) (dual of [2097176, 2097104, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12872, 2097173, F128, 23) (dual of [2097173, 2097101, 24]-code), using
- net defined by OOA [i] based on linear OOA(12872, 190652, F128, 23, 23) (dual of [(190652, 23), 4384924, 24]-NRT-code), using
(103, 126, 4754297)-Net over F16 — Digital
Digital (103, 126, 4754297)-net over F16, using
(103, 126, large)-Net in Base 16 — Upper bound on s
There is no (103, 126, large)-net in base 16, because
- 21 times m-reduction [i] would yield (103, 105, large)-net in base 16, but