Best Known (58−34, 58, s)-Nets in Base 128
(58−34, 58, 384)-Net over F128 — Constructive and digital
Digital (24, 58, 384)-net over F128, using
- 2 times m-reduction [i] based on digital (24, 60, 384)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 21, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 3 and N(F) ≥ 192, using
- net from sequence [i] based on digital (3, 191)-sequence over F128, using
- digital (3, 39, 192)-net over F128, using
- net from sequence [i] based on digital (3, 191)-sequence over F128 (see above)
- digital (3, 21, 192)-net over F128, using
- (u, u+v)-construction [i] based on
(58−34, 58, 408)-Net in Base 128 — Constructive
(24, 58, 408)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (1, 18, 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
- (6, 40, 258)-net in base 128, using
- base change [i] based on digital (1, 35, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 35, 258)-net over F256, using
- digital (1, 18, 150)-net over F128, using
(58−34, 58, 541)-Net over F128 — Digital
Digital (24, 58, 541)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12858, 541, F128, 34) (dual of [541, 483, 35]-code), using
- 146 step Varšamov–Edel lengthening with (ri) = (5, 0, 0, 1, 8 times 0, 1, 21 times 0, 1, 44 times 0, 1, 66 times 0) [i] based on linear OA(12849, 386, F128, 34) (dual of [386, 337, 35]-code), using
- extended algebraic-geometric code AGe(F,351P) [i] based on function field F/F128 with g(F) = 15 and N(F) ≥ 386, using
- 146 step Varšamov–Edel lengthening with (ri) = (5, 0, 0, 1, 8 times 0, 1, 21 times 0, 1, 44 times 0, 1, 66 times 0) [i] based on linear OA(12849, 386, F128, 34) (dual of [386, 337, 35]-code), using
(58−34, 58, 873860)-Net in Base 128 — Upper bound on s
There is no (24, 58, 873861)-net in base 128, because
- the generalized Rao bound for nets shows that 128m ≥ 165 266008 267600 098579 577143 743466 165988 568317 464986 730504 557165 378564 320269 995044 965348 511907 173172 634425 911348 044001 435744 > 12858 [i]