MinT - Best Known (212−101, 212, s)-Nets in Base 4

Best Known (212−101, 212, s)-Nets in Base 4

(212−101, 212, 130)-Net over F₄ — Constructive and digital

Digital (111, 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]

(212−101, 212, 176)-Net over F₄ — Digital

Digital (111, 212, 176)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−101, 212, 2214)-Net in Base 4 — Upper bound on s

There is no (111, 212, 2215)-net in base 4, because

1 times m-reduction [i] would yield (111, 211, 2215)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 934690 962042 891457 242425 371030 283049 320323 402897 331928 715492 571997 303059 906216 977760 779944 674901 369632 324327 462196 419805 256440 > 4²¹¹ [i]