MinT - Best Known (212−99, 212, s)-Nets in Base 4

Best Known (212−99, 212, s)-Nets in Base 4

(212−99, 212, 130)-Net over F₄ — Constructive and digital

Digital (113, 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]

(212−99, 212, 188)-Net over F₄ — Digital

Digital (113, 212, 188)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(212−99, 212, 2452)-Net in Base 4 — Upper bound on s

There is no (113, 212, 2453)-net in base 4, because

1 times m-reduction [i] would yield (113, 211, 2453)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 10 838273 695077 704933 223828 205072 437077 401273 703934 429389 175196 668852 719445 540825 278364 540844 143298 600093 220430 488266 798314 534208 > 4²¹¹ [i]