Best Known (16, 39, s)-Nets in Base 128
(16, 39, 345)-Net over F128 — Constructive and digital
Digital (16, 39, 345)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (5, 28, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- digital (0, 11, 129)-net over F128, using
(16, 39, 406)-Net over F128 — Digital
Digital (16, 39, 406)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12839, 406, F128, 23) (dual of [406, 367, 24]-code), using
- 19 step Varšamov–Edel lengthening with (ri) = (1, 18 times 0) [i] based on linear OA(12838, 386, F128, 23) (dual of [386, 348, 24]-code), using
- extended algebraic-geometric code AGe(F,362P) [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- 19 step Varšamov–Edel lengthening with (ri) = (1, 18 times 0) [i] based on linear OA(12838, 386, F128, 23) (dual of [386, 348, 24]-code), using
(16, 39, 407)-Net in Base 128 — Constructive
(16, 39, 407)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- (4, 27, 257)-net in base 128, using
- 5 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- base change [i] based on digital (0, 28, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 28, 257)-net over F256, using
- 5 times m-reduction [i] based on (4, 32, 257)-net in base 128, using
- digital (1, 12, 150)-net over F128, using
(16, 39, 513)-Net in Base 128
(16, 39, 513)-net in base 128, using
- 25 times m-reduction [i] based on (16, 64, 513)-net in base 128, using
- base change [i] based on digital (8, 56, 513)-net over F256, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- K1,1 from the tower of function fields by Niederreiter and Xing based on the tower by GarcÃa and Stichtenoth over F256 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 8 and N(F) ≥ 513, using
- net from sequence [i] based on digital (8, 512)-sequence over F256, using
- base change [i] based on digital (8, 56, 513)-net over F256, using
(16, 39, 735631)-Net in Base 128 — Upper bound on s
There is no (16, 39, 735632)-net in base 128, because
- 1 times m-reduction [i] would yield (16, 38, 735632)-net in base 128, but
- the generalized Rao bound for nets shows that 128m ≥ 118 572775 513213 262464 636504 859201 819384 948488 114934 962481 566543 261607 605420 110555 > 12838 [i]