Best Known (97, 97+25, s)-Nets in Base 4
(97, 97+25, 1055)-Net over F4 — Constructive and digital
Digital (97, 122, 1055)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (10, 22, 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 (75, 100, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 25, 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, 25, 257)-net over F256, using
- digital (10, 22, 27)-net over F4, using
(97, 97+25, 4293)-Net over F4 — Digital
Digital (97, 122, 4293)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4122, 4293, F4, 25) (dual of [4293, 4171, 26]-code), using
- 183 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 11 times 0, 1, 18 times 0, 1, 29 times 0, 1, 42 times 0, 1, 61 times 0) [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]
- 183 step Varšamov–Edel lengthening with (ri) = (4, 1, 1, 0, 0, 1, 4 times 0, 1, 6 times 0, 1, 11 times 0, 1, 18 times 0, 1, 29 times 0, 1, 42 times 0, 1, 61 times 0) [i] based on linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using
(97, 97+25, 2074960)-Net in Base 4 — Upper bound on s
There is no (97, 122, 2074961)-net in base 4, because
- 1 times m-reduction [i] would yield (97, 121, 2074961)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 7 067425 072465 683153 345244 318148 289285 996196 579702 227727 885607 251507 687468 > 4121 [i]