Best Known (74, 74+40, s)-Nets in Base 16
(74, 74+40, 587)-Net over F16 — Constructive and digital
Digital (74, 114, 587)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 26, 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 (48, 88, 522)-net over F16, using
- trace code for nets [i] based on digital (4, 44, 261)-net over F256, using
- net from sequence [i] based on digital (4, 260)-sequence over F256, using
- trace code for nets [i] based on digital (4, 44, 261)-net over F256, using
- digital (6, 26, 65)-net over F16, using
(74, 74+40, 612)-Net in Base 16 — Constructive
(74, 114, 612)-net in base 16, using
- (u, u+v)-construction [i] based on
- (14, 34, 98)-net in base 16, using
- 1 times m-reduction [i] based on (14, 35, 98)-net in base 16, using
- base change [i] based on digital (7, 28, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- base change [i] based on digital (7, 28, 98)-net over F32, using
- 1 times m-reduction [i] based on (14, 35, 98)-net in base 16, using
- digital (40, 80, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 40, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 40, 257)-net over F256, using
- (14, 34, 98)-net in base 16, using
(74, 74+40, 3794)-Net over F16 — Digital
Digital (74, 114, 3794)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16114, 3794, F16, 40) (dual of [3794, 3680, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(16114, 4107, F16, 40) (dual of [4107, 3993, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(36) [i] based on
- linear OA(16112, 4096, F16, 40) (dual of [4096, 3984, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [i]
- linear OA(16103, 4096, F16, 37) (dual of [4096, 3993, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(162, 11, F16, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(39) ⊂ Ce(36) [i] based on
- discarding factors / shortening the dual code based on linear OA(16114, 4107, F16, 40) (dual of [4107, 3993, 41]-code), using
(74, 74+40, 4042943)-Net in Base 16 — Upper bound on s
There is no (74, 114, 4042944)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 186070 855891 022456 190880 470384 593831 308353 811048 325482 766233 595959 920826 041192 469080 431188 779250 196630 044639 751306 087207 564897 900052 230701 > 16114 [i]