Best Known (202, 259, s)-Nets in Base 4
(202, 259, 1539)-Net over F4 — Constructive and digital
Digital (202, 259, 1539)-net over F4, using
- 41 times duplication [i] based on digital (201, 258, 1539)-net over F4, using
- t-expansion [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
- t-expansion [i] based on digital (200, 258, 1539)-net over F4, using
(202, 259, 4435)-Net over F4 — Digital
Digital (202, 259, 4435)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4259, 4435, F4, 57) (dual of [4435, 4176, 58]-code), using
- 332 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 14 times 0, 1, 40 times 0, 1, 72 times 0, 1, 94 times 0, 1, 103 times 0) [i] based on linear OA(4253, 4097, F4, 57) (dual of [4097, 3844, 58]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,28], and minimum distance d ≥ |{−28,−27,…,28}|+1 = 58 (BCH-bound) [i]
- 332 step Varšamov–Edel lengthening with (ri) = (1, 0, 0, 0, 1, 14 times 0, 1, 40 times 0, 1, 72 times 0, 1, 94 times 0, 1, 103 times 0) [i] based on linear OA(4253, 4097, F4, 57) (dual of [4097, 3844, 58]-code), using
(202, 259, 1328706)-Net in Base 4 — Upper bound on s
There is no (202, 259, 1328707)-net in base 4, because
- 1 times m-reduction [i] would yield (202, 258, 1328707)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 214526 782797 302920 738918 897639 496845 128383 674130 894619 336807 945985 405706 167022 645553 798842 984055 388189 036321 204363 729125 357277 048761 460947 060457 497602 488624 > 4258 [i]