Best Known (201−42, 201, s)-Nets in Base 4
(201−42, 201, 1060)-Net over F4 — Constructive and digital
Digital (159, 201, 1060)-net over F4, using
- 41 times duplication [i] based on digital (158, 200, 1060)-net over F4, using
- trace code for nets [i] based on digital (8, 50, 265)-net over F256, using
- net from sequence [i] based on digital (8, 264)-sequence over F256, using
- trace code for nets [i] based on digital (8, 50, 265)-net over F256, using
(201−42, 201, 4836)-Net over F4 — Digital
Digital (159, 201, 4836)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4201, 4836, F4, 42) (dual of [4836, 4635, 43]-code), using
- 720 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, 1, 52 times 0, 1, 74 times 0, 1, 99 times 0, 1, 122 times 0, 1, 139 times 0, 1, 152 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
- 720 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, 1, 52 times 0, 1, 74 times 0, 1, 99 times 0, 1, 122 times 0, 1, 139 times 0, 1, 152 times 0) [i] based on linear OA(4187, 4102, F4, 42) (dual of [4102, 3915, 43]-code), using
(201−42, 201, 1674715)-Net in Base 4 — Upper bound on s
There is no (159, 201, 1674716)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 10 329030 873034 843136 782431 390953 878623 057093 866508 270591 809961 406740 948496 276257 643993 174693 326439 763716 069303 781773 014046 > 4201 [i]