Best Known (97, 121, s)-Nets in Base 4
(97, 121, 1062)-Net over F4 — Constructive and digital
Digital (97, 121, 1062)-net over F4, using
- 41 times duplication [i] based on digital (96, 120, 1062)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (12, 24, 34)-net over F4, using
- trace code for nets [i] based on digital (0, 12, 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
- trace code for nets [i] based on digital (0, 12, 17)-net over F16, using
- digital (72, 96, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 24, 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, 24, 257)-net over F256, using
- digital (12, 24, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(97, 121, 4727)-Net over F4 — Digital
Digital (97, 121, 4727)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4121, 4727, F4, 24) (dual of [4727, 4606, 25]-code), using
- 618 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 9 times 0, 1, 17 times 0, 1, 28 times 0, 1, 44 times 0, 1, 69 times 0, 1, 101 times 0, 1, 143 times 0, 1, 190 times 0) [i] based on linear OA(4108, 4096, F4, 24) (dual of [4096, 3988, 25]-code), using
- 1 times truncation [i] based on linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using
- 618 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 4 times 0, 1, 9 times 0, 1, 17 times 0, 1, 28 times 0, 1, 44 times 0, 1, 69 times 0, 1, 101 times 0, 1, 143 times 0, 1, 190 times 0) [i] based on linear OA(4108, 4096, F4, 24) (dual of [4096, 3988, 25]-code), using
(97, 121, 2074960)-Net in Base 4 — Upper bound on s
There is no (97, 121, 2074961)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7 067425 072465 683153 345244 318148 289285 996196 579702 227727 885607 251507 687468 > 4121 [i]