Best Known (190, 190+54, s)-Nets in Base 4
(190, 190+54, 1056)-Net over F4 — Constructive and digital
Digital (190, 244, 1056)-net over F4, using
- trace code for nets [i] based on digital (7, 61, 264)-net over F256, using
- net from sequence [i] based on digital (7, 263)-sequence over F256, using
(190, 190+54, 4148)-Net over F4 — Digital
Digital (190, 244, 4148)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4244, 4148, F4, 54) (dual of [4148, 3904, 55]-code), using
- 43 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 9 times 0, 1, 30 times 0) [i] based on linear OA(4241, 4102, F4, 54) (dual of [4102, 3861, 55]-code), using
- construction X applied to Ce(53) ⊂ Ce(52) [i] based on
- linear OA(4241, 4096, F4, 54) (dual of [4096, 3855, 55]-code), using an extension Ce(53) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,53], and designed minimum distance d ≥ |I|+1 = 54 [i]
- linear OA(4235, 4096, F4, 53) (dual of [4096, 3861, 54]-code), using an extension Ce(52) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,52], and designed minimum distance d ≥ |I|+1 = 53 [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(53) ⊂ Ce(52) [i] based on
- 43 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 9 times 0, 1, 30 times 0) [i] based on linear OA(4241, 4102, F4, 54) (dual of [4102, 3861, 55]-code), using
(190, 190+54, 1004880)-Net in Base 4 — Upper bound on s
There is no (190, 244, 1004881)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 799 176930 217462 727142 104652 510583 009081 639085 970216 542499 861185 577858 984787 742730 192660 729311 753024 062857 804694 874392 981971 963618 775449 912528 533824 > 4244 [i]