MinT - Best Known (216−90, 216, s)-Nets in Base 4

Best Known (216−90, 216, s)-Nets in Base 4

(216−90, 216, 130)-Net over F₄ — Constructive and digital

Digital (126, 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]

(216−90, 216, 274)-Net over F₄ — Digital

Digital (126, 216, 274)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(216−90, 216, 4522)-Net in Base 4 — Upper bound on s

There is no (126, 216, 4523)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 11106 362597 078702 026458 368855 550777 344116 955268 448580 846180 736361 330283 736193 376340 434844 165245 624632 927135 252660 537171 188309 995584 > 4²¹⁶ [i]