Best Known (101, 101+26, s)-Nets in Base 4
(101, 101+26, 1055)-Net over F4 — Constructive and digital
Digital (101, 127, 1055)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (10, 23, 27)-net over F4, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 10 and N(F) ≥ 27, using
- net from sequence [i] based on digital (10, 26)-sequence over F4, using
- digital (78, 104, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 26, 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, 26, 257)-net over F256, using
- digital (10, 23, 27)-net over F4, using
(101, 101+26, 4286)-Net over F4 — Digital
Digital (101, 127, 4286)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4127, 4286, F4, 26) (dual of [4286, 4159, 27]-code), using
- 172 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 16 times 0, 1, 26 times 0, 1, 40 times 0, 1, 62 times 0) [i] based on linear OA(4115, 4102, F4, 26) (dual of [4102, 3987, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(4115, 4096, F4, 26) (dual of [4096, 3981, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(40, 6, F4, 0) (dual of [6, 6, 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(25) ⊂ Ce(24) [i] based on
- 172 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 16 times 0, 1, 26 times 0, 1, 40 times 0, 1, 62 times 0) [i] based on linear OA(4115, 4102, F4, 26) (dual of [4102, 3987, 27]-code), using
(101, 101+26, 1438615)-Net in Base 4 — Upper bound on s
There is no (101, 127, 1438616)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 28948 100212 342868 945383 371791 894588 646521 765450 840747 248606 710555 093300 295630 > 4127 [i]