Best Known (192, 246, s)-Nets in Base 4
(192, 246, 1539)-Net over F4 — Constructive and digital
Digital (192, 246, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 82, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
(192, 246, 4310)-Net over F4 — Digital
Digital (192, 246, 4310)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4246, 4310, F4, 54) (dual of [4310, 4064, 55]-code), using
- 203 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 9 times 0, 1, 30 times 0, 1, 65 times 0, 1, 93 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
- 203 step Varšamov–Edel lengthening with (ri) = (1, 0, 1, 9 times 0, 1, 30 times 0, 1, 65 times 0, 1, 93 times 0) [i] based on linear OA(4241, 4102, F4, 54) (dual of [4102, 3861, 55]-code), using
(192, 246, 1113556)-Net in Base 4 — Upper bound on s
There is no (192, 246, 1113557)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 12786 714212 722360 821520 316735 886316 714113 119672 356760 459508 100903 488686 721311 782515 405698 031197 663735 192082 266526 317990 561440 827868 495907 032075 122400 > 4246 [i]