Best Known (258−80, 258, s)-Nets in Base 2
(258−80, 258, 132)-Net over F2 — Constructive and digital
Digital (178, 258, 132)-net over F2, using
- trace code for nets [i] based on digital (49, 129, 66)-net over F4, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- net from sequence [i] based on digital (49, 65)-sequence over F4, using
(258−80, 258, 205)-Net over F2 — Digital
Digital (178, 258, 205)-net over F2, using
(258−80, 258, 1320)-Net in Base 2 — Upper bound on s
There is no (178, 258, 1321)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 473523 316238 975555 522199 546183 759473 560705 251417 944907 229198 833601 138606 144729 > 2258 [i]