Best Known (202, 260, s)-Nets in Base 4
(202, 260, 1539)-Net over F4 — Constructive and digital
Digital (202, 260, 1539)-net over F4, using
- 42 times duplication [i] based on digital (200, 258, 1539)-net over F4, using
- trace code for nets [i] based on digital (28, 86, 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
- trace code for nets [i] based on digital (28, 86, 513)-net over F64, using
(202, 260, 4157)-Net over F4 — Digital
Digital (202, 260, 4157)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4260, 4157, F4, 58) (dual of [4157, 3897, 59]-code), using
- 54 step Varšamov–Edel lengthening with (ri) = (1, 53 times 0) [i] based on linear OA(4259, 4102, F4, 58) (dual of [4102, 3843, 59]-code), using
- construction X applied to Ce(57) ⊂ Ce(56) [i] based on
- linear OA(4259, 4096, F4, 58) (dual of [4096, 3837, 59]-code), using an extension Ce(57) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,57], and designed minimum distance d ≥ |I|+1 = 58 [i]
- linear OA(4253, 4096, F4, 57) (dual of [4096, 3843, 58]-code), using an extension Ce(56) of the primitive narrow-sense BCH-code C(I) with length 4095 = 46−1, defining interval I = [1,56], and designed minimum distance d ≥ |I|+1 = 57 [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(57) ⊂ Ce(56) [i] based on
- 54 step Varšamov–Edel lengthening with (ri) = (1, 53 times 0) [i] based on linear OA(4259, 4102, F4, 58) (dual of [4102, 3843, 59]-code), using
(202, 260, 972230)-Net in Base 4 — Upper bound on s
There is no (202, 260, 972231)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 3 432405 731379 831909 516448 910550 704700 284914 462342 370428 204970 984387 315704 170204 785516 062866 085087 249164 359010 719370 883126 246469 786647 122327 694500 698848 223536 > 4260 [i]