Best Known (140−30, 140, s)-Nets in Base 4
(140−30, 140, 1048)-Net over F4 — Constructive and digital
Digital (110, 140, 1048)-net over F4, using
- trace code for nets [i] based on digital (5, 35, 262)-net over F256, using
- net from sequence [i] based on digital (5, 261)-sequence over F256, using
(140−30, 140, 3648)-Net over F4 — Digital
Digital (110, 140, 3648)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4140, 3648, F4, 30) (dual of [3648, 3508, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4140, 4127, F4, 30) (dual of [4127, 3987, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [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(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(47, 31, F4, 4) (dual of [31, 24, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(4140, 4127, F4, 30) (dual of [4127, 3987, 31]-code), using
(140−30, 140, 890976)-Net in Base 4 — Upper bound on s
There is no (110, 140, 890977)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 1 942693 756222 916261 609746 354258 006534 198987 547019 389050 769696 717298 318356 827526 149024 > 4140 [i]