Best Known (125−23, 125, s)-Nets in Base 16
(125−23, 125, 95391)-Net over F16 — Constructive and digital
Digital (102, 125, 95391)-net over F16, using
- 161 times duplication [i] based on digital (101, 124, 95391)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 17, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- digital (84, 107, 95326)-net over F16, using
- net defined by OOA [i] based on linear OOA(16107, 95326, F16, 23, 23) (dual of [(95326, 23), 2192391, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(16107, 1048587, F16, 23) (dual of [1048587, 1048480, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(20) [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]
- linear OA(1696, 1048576, F16, 21) (dual of [1048576, 1048480, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(161, 11, F16, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(22) ⊂ Ce(20) [i] based on
- OOA 11-folding and stacking with additional row [i] based on linear OA(16107, 1048587, F16, 23) (dual of [1048587, 1048480, 24]-code), using
- net defined by OOA [i] based on linear OOA(16107, 95326, F16, 23, 23) (dual of [(95326, 23), 2192391, 24]-NRT-code), using
- digital (6, 17, 65)-net over F16, using
- (u, u+v)-construction [i] based on
(125−23, 125, 190651)-Net in Base 16 — Constructive
(102, 125, 190651)-net in base 16, using
- base change [i] based on (77, 100, 190651)-net in base 32, using
- 322 times duplication [i] based on (75, 98, 190651)-net in base 32, using
- base change [i] based on digital (47, 70, 190651)-net over F128, using
- 1281 times duplication [i] based on digital (46, 69, 190651)-net over F128, using
- net defined by OOA [i] based on linear OOA(12869, 190651, F128, 23, 23) (dual of [(190651, 23), 4384904, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12869, 2097162, F128, 23) (dual of [2097162, 2097093, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(12869, 2097163, F128, 23) (dual of [2097163, 2097094, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- linear OA(12867, 2097152, F128, 23) (dual of [2097152, 2097085, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1282, 11, F128, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,128)), using
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- Reed–Solomon code RS(126,128) [i]
- discarding factors / shortening the dual code based on linear OA(1282, 128, F128, 2) (dual of [128, 126, 3]-code or 128-arc in PG(1,128)), using
- construction X applied to Ce(22) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(12869, 2097163, F128, 23) (dual of [2097163, 2097094, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12869, 2097162, F128, 23) (dual of [2097162, 2097093, 24]-code), using
- net defined by OOA [i] based on linear OOA(12869, 190651, F128, 23, 23) (dual of [(190651, 23), 4384904, 24]-NRT-code), using
- 1281 times duplication [i] based on digital (46, 69, 190651)-net over F128, using
- base change [i] based on digital (47, 70, 190651)-net over F128, using
- 322 times duplication [i] based on (75, 98, 190651)-net in base 32, using
(125−23, 125, 4191348)-Net over F16 — Digital
Digital (102, 125, 4191348)-net over F16, using
(125−23, 125, large)-Net in Base 16 — Upper bound on s
There is no (102, 125, large)-net in base 16, because
- 21 times m-reduction [i] would yield (102, 104, large)-net in base 16, but