Best Known (195−42, 195, s)-Nets in Base 4
(195−42, 195, 1052)-Net over F4 — Constructive and digital
Digital (153, 195, 1052)-net over F4, using
- 1 times m-reduction [i] based on digital (153, 196, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 49, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 49, 263)-net over F256, using
(195−42, 195, 4186)-Net over F4 — Digital
Digital (153, 195, 4186)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4195, 4186, F4, 42) (dual of [4186, 3991, 43]-code), using
- 76 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 11 times 0, 1, 19 times 0, 1, 33 times 0) [i] based on linear OA(4187, 4102, F4, 42) (dual of [4102, 3915, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(40) [i] based on
- linear OA(4187, 4096, F4, 42) (dual of [4096, 3909, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(4181, 4096, F4, 41) (dual of [4096, 3915, 42]-code), using an extension Ce(40) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,40], and designed minimum distance d ≥ |I|+1 = 41 [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(41) ⊂ Ce(40) [i] based on
- 76 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 0, 1, 5 times 0, 1, 11 times 0, 1, 19 times 0, 1, 33 times 0) [i] based on linear OA(4187, 4102, F4, 42) (dual of [4102, 3915, 43]-code), using
(195−42, 195, 1126994)-Net in Base 4 — Upper bound on s
There is no (153, 195, 1126995)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 2521 748565 642267 294176 829578 835588 971308 023955 538551 020007 493807 575669 487363 750271 553771 978568 569465 780841 624147 012704 > 4195 [i]