Best Known (90, 90+26, s)-Nets in Base 4
(90, 90+26, 1040)-Net over F4 — Constructive and digital
Digital (90, 116, 1040)-net over F4, using
- trace code for nets [i] based on digital (3, 29, 260)-net over F256, using
- net from sequence [i] based on digital (3, 259)-sequence over F256, using
(90, 90+26, 2488)-Net over F4 — Digital
Digital (90, 116, 2488)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4116, 2488, F4, 26) (dual of [2488, 2372, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4116, 4103, F4, 26) (dual of [4103, 3987, 27]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4115, 4102, F4, 26) (dual of [4102, 3987, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(4115, 4096, F4, 26) (dual of [4096, 3981, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4109, 4096, F4, 25) (dual of [4096, 3987, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(25) ⊂ Ce(24) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4115, 4102, F4, 26) (dual of [4102, 3987, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4116, 4103, F4, 26) (dual of [4103, 3987, 27]-code), using
(90, 90+26, 445145)-Net in Base 4 — Upper bound on s
There is no (90, 116, 445146)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 6901 750080 711946 696170 100760 072893 951034 715174 076320 809498 000529 027844 > 4116 [i]