Best Known (115, 115+71, s)-Nets in Base 4
(115, 115+71, 130)-Net over F4 — Constructive and digital
Digital (115, 186, 130)-net over F4, using
- t-expansion [i] based on digital (105, 186, 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
(115, 115+71, 321)-Net over F4 — Digital
Digital (115, 186, 321)-net over F4, using
(115, 115+71, 7025)-Net in Base 4 — Upper bound on s
There is no (115, 186, 7026)-net in base 4, because
- 1 times m-reduction [i] would yield (115, 185, 7026)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 2407 645635 177338 680306 877169 335591 135943 284346 024140 943956 903469 053819 566327 995588 652618 211353 723101 676142 690632 > 4185 [i]