Best Known (100, 127, s)-Nets in Base 4
(100, 127, 1045)-Net over F4 — Constructive and digital
Digital (100, 127, 1045)-net over F4, using
- 41 times duplication [i] based on digital (99, 126, 1045)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (5, 18, 17)-net over F4, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 5 and N(F) ≥ 17, using
- net from sequence [i] based on digital (5, 16)-sequence over F4, using
- digital (81, 108, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 27, 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, 27, 257)-net over F256, using
- digital (5, 18, 17)-net over F4, using
- (u, u+v)-construction [i] based on
(100, 127, 3652)-Net over F4 — Digital
Digital (100, 127, 3652)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4127, 3652, F4, 27) (dual of [3652, 3525, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(4127, 4121, F4, 27) (dual of [4121, 3994, 28]-code), using
- construction XX applied to Ce(26) ⊂ Ce(22) ⊂ Ce(21) [i] based on
- linear OA(4121, 4096, F4, 27) (dual of [4096, 3975, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(4103, 4096, F4, 23) (dual of [4096, 3993, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(497, 4096, F4, 22) (dual of [4096, 3999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(45, 24, F4, 3) (dual of [24, 19, 4]-code or 24-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(26) ⊂ Ce(22) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(4127, 4121, F4, 27) (dual of [4121, 3994, 28]-code), using
(100, 127, 1293100)-Net in Base 4 — Upper bound on s
There is no (100, 127, 1293101)-net in base 4, because
- 1 times m-reduction [i] would yield (100, 126, 1293101)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 7237 072602 485318 125166 620652 682089 798374 277223 691880 877358 451833 946056 996324 > 4126 [i]