Best Known (95−33, 95, s)-Nets in Base 16
(95−33, 95, 585)-Net over F16 — Constructive and digital
Digital (62, 95, 585)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (13, 29, 71)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (2, 10, 33)-net over F16, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 2 and N(F) ≥ 33, using
- net from sequence [i] based on digital (2, 32)-sequence over F16, using
- digital (3, 19, 38)-net over F16, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- net from sequence [i] based on digital (3, 37)-sequence over F16, using
- digital (2, 10, 33)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (33, 66, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 33, 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, 33, 257)-net over F256, using
- digital (13, 29, 71)-net over F16, using
(95−33, 95, 643)-Net in Base 16 — Constructive
(62, 95, 643)-net in base 16, using
- 161 times duplication [i] based on (61, 94, 643)-net in base 16, using
- (u, u+v)-construction [i] based on
- (12, 28, 129)-net in base 16, using
- base change [i] based on digital (0, 16, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- base change [i] based on digital (0, 16, 129)-net over F128, using
- digital (33, 66, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 33, 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, 33, 257)-net over F256, using
- (12, 28, 129)-net in base 16, using
- (u, u+v)-construction [i] based on
(95−33, 95, 3692)-Net over F16 — Digital
Digital (62, 95, 3692)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1695, 3692, F16, 33) (dual of [3692, 3597, 34]-code), using
- discarding factors / shortening the dual code based on linear OA(1695, 4112, F16, 33) (dual of [4112, 4017, 34]-code), using
- construction X applied to Ce(32) ⊂ Ce(27) [i] based on
- linear OA(1691, 4096, F16, 33) (dual of [4096, 4005, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(1679, 4096, F16, 28) (dual of [4096, 4017, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 4095 = 163−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(164, 16, F16, 4) (dual of [16, 12, 5]-code or 16-arc in PG(3,16)), using
- Reed–Solomon code RS(12,16) [i]
- construction X applied to Ce(32) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(1695, 4112, F16, 33) (dual of [4112, 4017, 34]-code), using
(95−33, 95, 5378382)-Net in Base 16 — Upper bound on s
There is no (62, 95, 5378383)-net in base 16, because
- 1 times m-reduction [i] would yield (62, 94, 5378383)-net in base 16, but
- 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]