Best Known (128, 128+111, s)-Nets in Base 4
(128, 128+111, 130)-Net over F4 — Constructive and digital
Digital (128, 239, 130)-net over F4, using
- t-expansion [i] based on digital (105, 239, 130)-net over F4, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 105 and N(F) ≥ 130, using
- T7 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) = 105 and N(F) ≥ 130, using
- net from sequence [i] based on digital (105, 129)-sequence over F4, using
(128, 128+111, 213)-Net over F4 — Digital
Digital (128, 239, 213)-net over F4, using
(128, 128+111, 2821)-Net in Base 4 — Upper bound on s
There is no (128, 239, 2822)-net in base 4, because
- 1 times m-reduction [i] would yield (128, 238, 2822)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 198163 608636 201322 306063 087923 997666 041117 185697 933282 720087 676558 545439 381444 438519 384175 970186 955170 873291 058346 823662 693151 117554 604625 272448 > 4238 [i]