Best Known (42−24, 42, s)-Nets in Base 64
(42−24, 42, 208)-Net over F64 — Constructive and digital
Digital (18, 42, 208)-net over F64, using
- (u, u+v)-construction [i] based on
- digital (3, 15, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 3 and N(F) ≥ 104, using
- net from sequence [i] based on digital (3, 103)-sequence over F64, using
- digital (3, 27, 104)-net over F64, using
- net from sequence [i] based on digital (3, 103)-sequence over F64 (see above)
- digital (3, 15, 104)-net over F64, using
(42−24, 42, 288)-Net in Base 64 — Constructive
(18, 42, 288)-net in base 64, using
- 21 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on digital (9, 54, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 54, 288)-net over F128, using
(42−24, 42, 314)-Net over F64 — Digital
Digital (18, 42, 314)-net over F64, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(6442, 314, F64, 24) (dual of [314, 272, 25]-code), using
- 51 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 0, 1, 13 times 0, 1, 32 times 0) [i] based on linear OA(6436, 257, F64, 24) (dual of [257, 221, 25]-code), using
- extended algebraic-geometric code AGe(F,232P) [i] based on function field F/F64 with g(F) = 12 and N(F) ≥ 257, using
- 51 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 0, 1, 13 times 0, 1, 32 times 0) [i] based on linear OA(6436, 257, F64, 24) (dual of [257, 221, 25]-code), using
(42−24, 42, 321)-Net in Base 64
(18, 42, 321)-net in base 64, using
- base change [i] based on digital (12, 36, 321)-net over F128, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 12 and N(F) ≥ 321, using
- net from sequence [i] based on digital (12, 320)-sequence over F128, using
(42−24, 42, 176050)-Net in Base 64 — Upper bound on s
There is no (18, 42, 176051)-net in base 64, because
- the generalized Rao bound for nets shows that 64m ≥ 7237 357614 248000 445977 419079 973477 152705 827202 492868 599363 041387 900087 488316 > 6442 [i]