Best Known (113, 143, s)-Nets in Base 4
(113, 143, 1049)-Net over F4 — Constructive and digital
Digital (113, 143, 1049)-net over F4, using
- 41 times duplication [i] based on digital (112, 142, 1049)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (7, 22, 21)-net over F4, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 7 and N(F) ≥ 21, using
- net from sequence [i] based on digital (7, 20)-sequence over F4, using
- digital (90, 120, 1028)-net over F4, using
- trace code for nets [i] based on digital (0, 30, 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, 30, 257)-net over F256, using
- digital (7, 22, 21)-net over F4, using
- (u, u+v)-construction [i] based on
(113, 143, 4181)-Net over F4 — Digital
Digital (113, 143, 4181)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4143, 4181, F4, 30) (dual of [4181, 4038, 31]-code), using
- 69 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 10 times 0, 1, 16 times 0, 1, 26 times 0) [i] based on linear OA(4133, 4102, F4, 30) (dual of [4102, 3969, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(28) [i] based on
- linear OA(4133, 4096, F4, 30) (dual of [4096, 3963, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4127, 4096, F4, 29) (dual of [4096, 3969, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(29) ⊂ Ce(28) [i] based on
- 69 step Varšamov–Edel lengthening with (ri) = (3, 1, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 10 times 0, 1, 16 times 0, 1, 26 times 0) [i] based on linear OA(4133, 4102, F4, 30) (dual of [4102, 3969, 31]-code), using
(113, 143, 1175654)-Net in Base 4 — Upper bound on s
There is no (113, 143, 1175655)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 124 332346 659523 472010 705293 518675 130726 647545 243231 891355 266057 688700 629626 258585 763504 > 4143 [i]