MinT - Best Known (212−95, 212, s)-Nets in Base 4

Best Known (212−95, 212, s)-Nets in Base 4

(212−95, 212, 130)-Net over F₄ — Constructive and digital

Digital (117, 212, 130)-net over F₄, using

t-expansion [i] based on digital (105, 212, 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]

(212−95, 212, 213)-Net over F₄ — Digital

Digital (117, 212, 213)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−95, 212, 3050)-Net in Base 4 — Upper bound on s

There is no (117, 212, 3051)-net in base 4, because

1 times m-reduction [i] would yield (117, 211, 3051)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 880829 023562 427279 920343 672174 669896 447122 637324 870742 553388 580265 237935 924993 215368 522813 426983 995045 504681 133706 186847 802240 > 4²¹¹ [i]