MinT - Best Known (216−95, 216, s)-Nets in Base 4

Best Known (216−95, 216, s)-Nets in Base 4

(216−95, 216, 130)-Net over F₄ — Constructive and digital

Digital (121, 216, 130)-net over F₄, using

t-expansion [i] based on digital (105, 216, 130)-net over F₄, using
- net from sequence [i] based on digital (105, 129)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ 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]

(216−95, 216, 230)-Net over F₄ — Digital

Digital (121, 216, 230)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−95, 216, 3437)-Net in Base 4 — Upper bound on s

There is no (121, 216, 3438)-net in base 4, because

1 times m-reduction [i] would yield (121, 215, 3438)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 2790 833680 388830 436095 556271 209615 326439 482276 135319 635944 360061 040384 686957 765262 989027 417009 177029 845074 133393 726175 832424 642800 > 4²¹⁵ [i]