Best Known (130−28, 130, s)-Nets in Base 16
(130−28, 130, 9427)-Net over F16 — Constructive and digital
Digital (102, 130, 9427)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (6, 20, 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 (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 (6, 20, 65)-net over F16, using
(130−28, 130, 18726)-Net in Base 16 — Constructive
(102, 130, 18726)-net in base 16, using
- net defined by OOA [i] based on OOA(16130, 18726, S16, 28, 28), using
- OA 14-folding and stacking [i] based on OA(16130, 262164, S16, 28), using
- 1 times code embedding in larger space [i] based on OA(16129, 262163, S16, 28), using
- discarding parts of the base [i] based on linear OA(6486, 262163, F64, 28) (dual of [262163, 262077, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] 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]
- linear OA(6467, 262144, F64, 23) (dual of [262144, 262077, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(644, 19, F64, 4) (dual of [19, 15, 5]-code or 19-arc in PG(3,64)), using
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- Reed–Solomon code RS(60,64) [i]
- discarding factors / shortening the dual code based on linear OA(644, 64, F64, 4) (dual of [64, 60, 5]-code or 64-arc in PG(3,64)), using
- construction X applied to Ce(27) ⊂ Ce(22) [i] based on
- discarding parts of the base [i] based on linear OA(6486, 262163, F64, 28) (dual of [262163, 262077, 29]-code), using
- 1 times code embedding in larger space [i] based on OA(16129, 262163, S16, 28), using
- OA 14-folding and stacking [i] based on OA(16130, 262164, S16, 28), using
(130−28, 130, 457028)-Net over F16 — Digital
Digital (102, 130, 457028)-net over F16, using
(130−28, 130, large)-Net in Base 16 — Upper bound on s
There is no (102, 130, large)-net in base 16, because
- 26 times m-reduction [i] would yield (102, 104, large)-net in base 16, but