Best Known (110−37, 110, s)-Nets in Base 16
(110−37, 110, 1028)-Net over F16 — Constructive and digital
Digital (73, 110, 1028)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (18, 36, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 18, 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, 18, 257)-net over F256, using
- digital (37, 74, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 37, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 37, 257)-net over F256, using
- digital (18, 36, 514)-net over F16, using
(110−37, 110, 4589)-Net over F16 — Digital
Digital (73, 110, 4589)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16110, 4589, F16, 37) (dual of [4589, 4479, 38]-code), using
- 483 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 15 times 0, 1, 55 times 0, 1, 144 times 0, 1, 261 times 0) [i] based on linear OA(16103, 4099, F16, 37) (dual of [4099, 3996, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(35) [i] based on
- 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(16100, 4096, F16, 36) (dual of [4096, 3996, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(160, 3, F16, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(36) ⊂ Ce(35) [i] based on
- 483 step Varšamov–Edel lengthening with (ri) = (3, 0, 0, 0, 1, 15 times 0, 1, 55 times 0, 1, 144 times 0, 1, 261 times 0) [i] based on linear OA(16103, 4099, F16, 37) (dual of [4099, 3996, 38]-code), using
(110−37, 110, large)-Net in Base 16 — Upper bound on s
There is no (73, 110, large)-net in base 16, because
- 35 times m-reduction [i] would yield (73, 75, large)-net in base 16, but