Best Known (125−25, 125, s)-Nets in Base 4
(125−25, 125, 1062)-Net over F4 — Constructive and digital
Digital (100, 125, 1062)-net over F4, using
- 41 times duplication [i] based on digital (99, 124, 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 (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 (12, 24, 34)-net over F4, using
- (u, u+v)-construction [i] based on
(125−25, 125, 4655)-Net over F4 — Digital
Digital (100, 125, 4655)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4125, 4655, F4, 25) (dual of [4655, 4530, 26]-code), using
- 542 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, 1, 86 times 0, 1, 117 times 0, 1, 153 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]
- 542 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, 1, 86 times 0, 1, 117 times 0, 1, 153 times 0) [i] based on linear OA(4109, 4097, F4, 25) (dual of [4097, 3988, 26]-code), using
(125−25, 125, 2934440)-Net in Base 4 — Upper bound on s
There is no (100, 125, 2934441)-net in base 4, because
- 1 times m-reduction [i] would yield (100, 124, 2934441)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 452 313498 107979 922855 712623 300076 475677 994123 383030 803717 000410 324104 143240 > 4124 [i]