Best Known (62, 94, s)-Nets in Base 16
(62, 94, 596)-Net over F16 — Constructive and digital
Digital (62, 94, 596)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (14, 30, 82)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 8, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (6, 22, 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 (0, 8, 17)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (32, 64, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 32, 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, 32, 257)-net over F256, using
- digital (14, 30, 82)-net over F16, using
(62, 94, 664)-Net in Base 16 — Constructive
(62, 94, 664)-net in base 16, using
- (u, u+v)-construction [i] based on
- (14, 30, 150)-net in base 16, using
- base change [i] based on (4, 20, 150)-net in base 64, using
- 1 times m-reduction [i] based on (4, 21, 150)-net in base 64, using
- base change [i] based on digital (1, 18, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 18, 150)-net over F128, using
- 1 times m-reduction [i] based on (4, 21, 150)-net in base 64, using
- base change [i] based on (4, 20, 150)-net in base 64, using
- digital (32, 64, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 32, 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, 32, 257)-net over F256, using
- (14, 30, 150)-net in base 16, using
(62, 94, 4138)-Net over F16 — Digital
Digital (62, 94, 4138)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1694, 4138, F16, 32) (dual of [4138, 4044, 33]-code), using
- 38 step Varšamov–Edel lengthening with (ri) = (2, 1, 6 times 0, 1, 29 times 0) [i] based on linear OA(1690, 4096, F16, 32) (dual of [4096, 4006, 33]-code), using
- 1 times truncation [i] based on linear OA(1691, 4097, F16, 33) (dual of [4097, 4006, 34]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 166−1, defining interval I = [0,16], and minimum distance d ≥ |{−16,−15,…,16}|+1 = 34 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(1691, 4097, F16, 33) (dual of [4097, 4006, 34]-code), using
- 38 step Varšamov–Edel lengthening with (ri) = (2, 1, 6 times 0, 1, 29 times 0) [i] based on linear OA(1690, 4096, F16, 32) (dual of [4096, 4006, 33]-code), using
(62, 94, 5378382)-Net in Base 16 — Upper bound on s
There is no (62, 94, 5378383)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 153914 390711 462581 699662 033282 009576 415684 696425 504862 653704 456701 370481 416526 586604 780819 047490 470320 278363 655796 > 1694 [i]