Best Known (36, 36+14, s)-Nets in Base 4
(36, 36+14, 240)-Net over F4 — Constructive and digital
Digital (36, 50, 240)-net over F4, using
- t-expansion [i] based on digital (35, 50, 240)-net over F4, using
- 1 times m-reduction [i] based on digital (35, 51, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 17, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 17, 80)-net over F64, using
- 1 times m-reduction [i] based on digital (35, 51, 240)-net over F4, using
(36, 36+14, 258)-Net in Base 4 — Constructive
(36, 50, 258)-net in base 4, using
- trace code for nets [i] based on (11, 25, 129)-net in base 16, using
- base change [i] based on (6, 20, 129)-net in base 32, using
- 1 times m-reduction [i] based on (6, 21, 129)-net in base 32, using
- base change [i] based on digital (0, 15, 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, 15, 129)-net over F128, using
- 1 times m-reduction [i] based on (6, 21, 129)-net in base 32, using
- base change [i] based on (6, 20, 129)-net in base 32, using
(36, 36+14, 398)-Net over F4 — Digital
Digital (36, 50, 398)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(450, 398, F4, 14) (dual of [398, 348, 15]-code), using
- 129 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 16 times 0, 1, 23 times 0, 1, 30 times 0, 1, 36 times 0) [i] based on linear OA(441, 260, F4, 14) (dual of [260, 219, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(441, 256, F4, 14) (dual of [256, 215, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(437, 256, F4, 13) (dual of [256, 219, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(40, 4, F4, 0) (dual of [4, 4, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- 129 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 16 times 0, 1, 23 times 0, 1, 30 times 0, 1, 36 times 0) [i] based on linear OA(441, 260, F4, 14) (dual of [260, 219, 15]-code), using
(36, 36+14, 22496)-Net in Base 4 — Upper bound on s
There is no (36, 50, 22497)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 267684 133317 045680 551473 574560 > 450 [i]