MinT - Best Known (214−101, 214, s)-Nets in Base 4

Best Known (214−101, 214, s)-Nets in Base 4

(214−101, 214, 130)-Net over F₄ — Constructive and digital

Digital (113, 214, 130)-net over F₄, using

t-expansion [i] based on digital (105, 214, 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]

(214−101, 214, 183)-Net over F₄ — Digital

Digital (113, 214, 183)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(214−101, 214, 2343)-Net in Base 4 — Upper bound on s

There is no (113, 214, 2344)-net in base 4, because

1 times m-reduction [i] would yield (113, 213, 2344)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 176 388925 004059 728506 898739 207801 429129 314004 121277 405342 799969 014975 263632 079179 305568 317997 076948 495295 990196 579881 588984 528400 > 4²¹³ [i]