Best Known (151−30, 151, s)-Nets in Base 2
(151−30, 151, 260)-Net over F2 — Constructive and digital
Digital (121, 151, 260)-net over F2, using
- t-expansion [i] based on digital (120, 151, 260)-net over F2, using
- 1 times m-reduction [i] based on digital (120, 152, 260)-net over F2, using
- trace code for nets [i] based on digital (6, 38, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- trace code for nets [i] based on digital (6, 38, 65)-net over F16, using
- 1 times m-reduction [i] based on digital (120, 152, 260)-net over F2, using
(151−30, 151, 463)-Net over F2 — Digital
Digital (121, 151, 463)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2151, 463, F2, 2, 30) (dual of [(463, 2), 775, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2151, 517, F2, 2, 30) (dual of [(517, 2), 883, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2151, 1034, F2, 30) (dual of [1034, 883, 31]-code), using
- 1 times truncation [i] based on linear OA(2152, 1035, F2, 31) (dual of [1035, 883, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- linear OA(2151, 1024, F2, 31) (dual of [1024, 873, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(2141, 1024, F2, 29) (dual of [1024, 883, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 1023 = 210−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(21, 11, F2, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(30) ⊂ Ce(28) [i] based on
- 1 times truncation [i] based on linear OA(2152, 1035, F2, 31) (dual of [1035, 883, 32]-code), using
- OOA 2-folding [i] based on linear OA(2151, 1034, F2, 30) (dual of [1034, 883, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(2151, 517, F2, 2, 30) (dual of [(517, 2), 883, 31]-NRT-code), using
(151−30, 151, 6866)-Net in Base 2 — Upper bound on s
There is no (121, 151, 6867)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 2856 361081 950609 466616 012545 684069 736320 414568 > 2151 [i]